# 5.4: Four Operations with Rational Numbers - Mathematics

5.4: Four Operations with Rational Numbers - Mathematics

## Need Math Help

In abstract algebra, the concept of a polynomial is extended to include formal expressions in which the coefficients of the polynomial can be taken from any field. In this setting given a field F and some indeterminate X, a rational expression is any element of the field of fractions of the polynomial ring F[X].

Source: Wikipedia
Concept of Rational Number System:

Rational number is the quotient of two integers. Therefore, a rational number is a number that can be write in the form s/t, where s and t are integers, and t is not zero. A rational number written in this way is commonly called a fraction.

12/15,(-7)/(9x) rArr Rational numbers

An integer can be marking it as the quotient of the integer and 1, every integer is a rational number.
Example Problem for Operations with Rational Number System:

A rational number written as a fraction can be written in decimal notation.

Solution:
11 rArr This is called a terminating decimal.
3 | 33
3
3
3
0rArr The remainder is Zero.

Adding operations in rational number system with same denominators:

Adding operations in rational number system with different denominators:

Just as we add fractions, rational numbers with different denominators can also be extra. By finding out the LCM, we can take the denominators to the same number.

Subtraction operations in rational number system with same denominators:

Just as we subtract fractions, we can subtract rational numbers with same denominator.

Subtraction operations in rational number system with different denominators:

Just as we subtract fractions, rational numbers also can be taken off with different denominators. The common denominator is achieved by finding out the LCM.

Multiplication operations in rational number system with same denominators:

Just alike the multiplication of whole numbers and integers, multiplication of rational number are also repeated addition.

Multiplication operations in rational number system with different denominators:

Here, for both the fractions, we have the same denominator, we have to take only one denominator and add the numerators.

Here, for both the fractions, we have the same denominator, we have to take only one denominator and subtract the numerators.

In the given two fractions, denominators are 8 and 3.

For 8 and 3, there is no common divisor other than 1.

Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below. In the given two fractions, denominators are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

So 12 and 20 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 12 and 20.

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 =ਂ² x 3 x 5

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as given below. Convert the fraction 17/5 into mixed number.

The picture given below clearly illustrates, how to convert the fraction 17/5 into mixed number. To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators.

To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

Lily earned $54 mowing lawns in two days. She worked 2.5 hours yesterday and 4.25 hours today. If Naomi was paid the same amount for every hour she works, how much did she earn per hour ? Identify the important information. • Naomi made$54 mowing lawns.

• Naomi worked 2.5 hours yesterday and 4.25 hours today.

• We are asked to find how much she earned per hour

• The total amount she earned divided by the total hours she worked  gives the amount she earns per hour.

• Use the expression 54 ÷ (2.5 + 4.25) to find the amount she earned  per hour.

(2.5 + 4.25)  = ਆ.75  ---- > ( Add inside parentheses)

Lily earned $8 per hour mowing lawns. David traveled from A to B in 3 hours at the rate of 50 miles per hour. Then he traveled from B to C in 2 hours at the rate of 60 miles per hour. What is the average speed of David from A to C ? Identify the important information. • David traveled from A to B in 3 hours @ 50 mph. • David traveled from B to C in 2 hours @ 60 mph. • We are asked to find the average speed from A to C. • The total distance covered from A to C divided by total time taken gives the average speed from A to C. • Use the expression (3 x 50) + (2 x 60) to find the total distance from A to C . • Use the expression (3 + 2) to find the total time taken from A to C. Divide the total distance (A to C) by the total time taken (A to C) So, the average speed from A to C is 54 miles per hour. Each part of a multipart question on a test is worth the same number of points. The whole question is worth 37.5 points. Daniel got 1/2 of the parts of a question correct. How many points did Daniel receive ? To find the total points received by Daniel, we have to multiply 1/2 and 37.5 Convert the decimal 3.75 as the fraction 75/2 Multiply. Write the product in simplest form. So, Daniel received 18 3/4 points. The bill for a pizza was$14.50. Charles paid for 3/5 of the bill. How much did he pay ?

To find the amount paid by Charles, we have to multiply 3/5 and 14.50

Convert the decimal 14.50 as the fraction 29/2

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## Mathematics Solutions for Class 7 Maths Chapter 5 - Operations On Rational Numbers

Mathematics Solutions Solutions for Class 7 Maths Chapter 5 Operations On Rational Numbers are provided here with simple step-by-step explanations. These solutions for Operations On Rational Numbers are extremely popular among Class 7 students for Maths Operations On Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 7 Maths Chapter 5 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 7 Maths are prepared by experts and are 100% accurate.

#### Question 1:

Carry out the following additions of rational numbers.

i   5 36 + 6 42
At first, we will calculate the LCM of 36 and 42. The prime factorisation is 36 and 42 is,
36 = 2 × 2 × 3 × 3
42 = 2 × 3 × 7
Now, LCM of 36 and 42 = 2 × 2 × 3 × 3 × 7 = 252
5 36 + 6 42 = 5 × 7 36 × 7 + 6 × 6 42 × 6 = 35 252 + 36 252 = 35 + 36 252 = 71 252
ii   1 2 3 + 2 4 5 = 1 × 3 + 2 3 + 2 × 5 + 4 5 = 5 3 + 14 5
Now, LCM of 3 and 5 is 15.
5 3 + 14 5 = 5 × 5 3 × 5 + 14 × 3 5 × 3 = 25 15 + 42 15 = 67 15 = 4 7 15
iii   11 17 + 13 19
Now, LCM of 17 and 19 is 323.
11 17 + 13 19 = 11 × 19 17 × 19 + 13 × 17 19 × 17 = 209 323 + 221 323 = 430 323
iv   2 3 11 + 1 3 77 = 2 × 11 + 3 11 + 1 × 77 + 3 77 = 25 11 + 80 77
Now, LCM of 11 and 77 is 77.
25 11 + 80 77 = 25 × 7 11 × 7 + 80 × 1 77 × 1 = 175 77 + 80 77 = 255 77 = 3 24 77

#### Question 2:

Carry out the following subtarctions involving rational numbers.

i   7 11 - 3 7
Now, LCM of 11 and 7 is 77.
7 11 - 3 7 = 7 × 7 11 × 7 - 3 × 11 7 × 11 = 49 77 - 33 77 = 49 - 33 77 = 16 77
ii   13 36 - 2 40
Now, LCM of 36 and 40 is 360.
13 36 - 2 40 = 13 × 10 36 × 10 - 2 × 9 40 × 9 = 130 360 - 18 360 = 130 - 18 360 = 112 360 = 112 ÷ 8 360 ÷ 8         since ,   HCF   of   112   and   360   is   8 = 14 45
iii   1 2 3 - 3 5 6 = 1 × 3 + 2 3 - 3 × 6 + 5 6 = 5 3 - 23 6
Now, LCM of 3 and 6 is 6.
5 3 - 23 6 = 5 × 2 3 × 2 - 23 × 1 6 × 1 = 10 6 - 23 6 = 10 - 23 6 = - 13 6
iv   4 1 2 - 3 1 3 = 4 × 2 + 1 2 - 3 × 3 + 1 3 = 9 2 - 10 3
Now, LCM of 2 and 3 is 6.
9 2 - 10 3 = 9 × 3 2 × 3 - 10 × 2 3 × 2 = 18 6 - 20 6 = 18 - 20 6 = - 2 6 = - 1 3

#### Question 3:

Multiply the following rational numbers.

i   3 11 × 2 5 = 3 × 2 11 × 5 = 6 55
ii   12 5 × 4 15 = 12 × 4 5 × 15 = 48 75 = 48 ÷ 3 75 ÷ 3         Since ,   HCF   of   48   and   75   is   3 = 16 25
iii   - 8 9 × 3 4 = - 8 × 3 9 × 4 = - 24 36 = - 24 ÷ 12 36 ÷ 12         Since ,   HCF   of   24   and   36   is   12 = - 2 3
iv   0 6 × 3 4 = 0 × 3 6 × 4 = 0 24 = 0

#### Question 4:

Write the multiplicative inverse.

It is known that, the multiplicative inverse of any rational number a is the reciprocal of the rational number i.e., 1 a .
(i) Multiplicative inverse of 2 5 = 1 2 5 = 5 2
(ii) Multuplicative inverse of - 3 8 = 1 - 3 8 = - 8 3
(iii) Multiplicative inverse of - 17 39 = 1 - 17 39 = - 39 17
(iv) Multiplicative inverse of 7 = 1 7
(v) The given number is - 7 1 3 .
Now ,   - 7 1 3 = - 7 + 1 3 = - 21 + 1 3 = - 22 3
Multiplicative inverse of - 22 3 = 1 - 22 3 = - 3 22

#### Question 5:

Carry out the divisions of rational numbers.

i   40 12 ÷ 10 4 = 40 12 × 4 10 = 40 × 4 12 × 10 = 160 120 = 160 ÷ 40 120 ÷ 40         Since ,   HCF   of   160   and   120   is   40 = 40 3
ii   - 10 11 ÷ - 11 10 = - 10 11 × - 10 11 = - 10 × - 10 11 × 11 = 100 121
iii   - 7 8 ÷ - 3 6 = - 7 8 × - 6 3 = - 7 × - 6 8 × 3 = 42 24 = 42 ÷ 6 24 ÷ 6         Since ,   HCF   of   42   and   24   is   6       = 7 4
iv   2 3 ÷ - 4 = 2 3 × - 1 4 = 2 × - 1 3 × 4 = - 2 12 = - 2 ÷ 2 12 ÷ 2         Since ,   HCF   of   2   and   12   is   2 = - 1 6
v   2 1 5 ÷ 5 3 6 = 2 × 5 + 1 5 ÷ 5 × 6 + 3 6 = 11 5 ÷ 33 6 = 11 5 × 6 33 = 11 × 6 5 × 33 = 66 165 = 66 ÷ 33 165 ÷ 33         Since ,   HCF   of   66   and   165   is   33     = 2 5

#### Question 1:

Write three rational numbers that lie between the two given numbers.

(i) The given numbers are 2 7 and 6 7 .
We know that,
2 < 3 < 4 < 5 < 6
∴   2 7 < 3 7 < 4 7 < 5 7 < 6 7
Hence, 3 rational numbers between 2 7 and 6 7 are :
3 7 , 4 7 and 5 7 .

(ii) The given numbers are 4 5 and 2 3 .
Let us convert these numbers into fractions with equal denominators.
4 5 = 4 × 6 5 × 6 = 24 30 2 3 = 2 × 10 3 × 10 = 20 30
We know that,
20 < 21 < 22 < 23 < 24
∴   20 30 < 21 30 < 22 30 < 23 30 < 24 30 ⇒ 2 3 < 21 30 < 22 30 < 23 30 < 4 5
Hence, 3 rational numbers between 2 3 and 4 5 are :
21 30 , 22 30 and 23 30 .

(iii) The given numbers are - 2 3 and 4 5 .
Let us convert each of given numbers into fractions with equal denominators.
- 2 3 = - 2 × 5 3 × 5 = - 10 15 4 5 = 4 × 3 5 × 3 = 12 15
We know that,
&minus10 < &minus9 < &minus8 < &minus7 <. < 1 < 2 < 3 < 4 <. < 12
⇒   - 2 3 < - 9 15 < - 8 15 < - 7 15 < . . . . . < 1 15 < 2 15 < 3 15 < 4 15 < . . . . . < 4 15
Hence, 3 rational numbers between - 2 3 and 4 5 are:
- 9 15 , - 7 15 and 4 15 .

(iv) The given numbers are 7 9 and - 5 9 .
We know that,
&minus5 < &minus4 < &minus3 < &minus2 < &minus1 < 0 <. < 6 < 7
∴   - 5 9 < - 4 9 < - 3 9 < - 2 9 < - 1 9 < 0 < . . . . . < 6 9 < 7 9
Hence, 3 rational numbers between - 5 9 and 7 9 are:
- 4 9 ,   0 and 6 9 .

(v) The given numbers are - 3 4 and 5 4 .
We know that,
&minus3 < &minus2 < &minus1 < 0 < 1 < 2 < 3 < 4 < 5
∴   - 3 4 < - 2 4 < - 1 4 < 0 < 1 4 < 2 4 < 3 4 < 4 4 < 5 4
Hence, 3 rational numbers between - 3 4 and 5 4 are:
- 2 4 ,   - 1 4 and 3 4 .

(vi) The given numbers are 7 8 and - 5 3 .
Let us convert each of the given numbers into fractions with equal denominators.
7 8 = 7 × 3 8 × 3 = 21 24 - 5 3 = - 5 × 8 3 × 8 = - 40 24
We know that,
&minus40 < &minus39 <. < &minus13 < &minus12 <. <11 < 12 <. 17 <. 21
∴   - 40 24 < - 39 24 < . . . . . < - 13 24 < - 12 24 < . . . . < 11 24 < 12 24 < . . . . < 17 24 < . . . . < 21 24 ⇒   - 5 3 < - 39 24 < . . . . . . < - 13 24 < - 12 24 < . . . . < 11 24 < 12 24 < . . . . < 17 24 < . . . . < 7 8
Hence, 3 rational numbers between - 5 3 and 7 8 are:
- 13 24 ,   11 24 and 17 24 .

(vii) The given numbers are 5 7 and 11 7 .
We know that,
5 < 6 < 7 < 8 < 9 < 10 < 11
∴ 5 7 < 6 7 < 7 7 < 8 7 < 9 7 < 10 7 < 11 7
Hence, 3 rational numbers between 5 7 and 11 7 are :
6 7 , 8 7 and 9 7

(viii) The given numbers are 0 and - 3 4 .
Let us convert each of the given numbers into fractions with equal denominators.
0 = 0 × 8 1 × 8 = 0 8 - 3 4 = - 3 × 2 4 × 2 = - 6 8
We know that,
&minus6 < &minus5 < &minus4 < &minus3 < &minus2 < &minus1 < 0
∴   - 6 8 < - 5 8 < - 4 8 < - 3 8 < - 2 8 < - 1 8 < 0 8 ⇒   - 3 4 < - 5 8 < - 4 8 < - 3 8 < - 2 8 < - 1 8 < 0
Hence, 3 rational numbers between - 6 8 and 0 are:
- 5 8 ,   - 2 8 and - 1 8 .

## IM Commentary

This task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality. As such, this task perhaps makes most sense after students learn the key terms (rational and irrational numbers), as well as examples of each (e.g., the irrationality of $sqrt<2>$, $pi$, etc.), but before formally proving any of the statements to be discovered in this task. Discussion of such proofs is taken up in other tasks.

These conjectures are likely best discussed in small groups and/or with the whole class, and so is best used in instructional, rather than assessment-based, settings. The discussions generated by student conjectures will likely yield productive insights into the nature of sums and products of real numbers leading eventually to the explanations sought in content standard N.RN.3, preparing them for the formal statements of these results. Note that some of these decisions, e.g., the irrationality of $pi+sqrt<2>$, are well beyond the scope of high school mathematics, but this does not preclude students from being able to answer the always/sometimes/never questions being asked.

Learning Domain: The Number System

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Indicator: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

## Sequencing of Mathematical Operations

So far in this mathematic review for your TEAS examination, you have worked with calculations with only one operation. For example, you worked with only addition, only subtraction, only multiplication and only division, however, you have to also know how to perform several basic arithmetic operations in one calculation problem. For example, you may have to add and multiply in one calculation you may have to both multiply and divide in the same calculation and you may also have to add, subtract, multiply and divide in addition to performing calculations that are within parentheses.

In this section, you will learn how to do these problems using the correct sequencing of multiple basic arithmetic calculations. Which one would you do first? Which mathematical calculation would you do second, etc.? If these calculations are NOT done in the correct sequence, your answer will be wrong and incorrect.

The correct sequence for performing several mathematic operations from the first to the last are:

1. Calculating all the operations that are in parentheses
2. Calculating multiplication and division starting from the left and moving to the right
3. Calculating addition and subtraction starting from the left and moving to the right

You can remember this sequence with the PMDAS acronym for Parentheses – Multiplication – Division - Addition and Subtraction: "Performing Math Doing A Sequence" when you are taking your TEAS examination.

See the calculations below to learn how to perform several basic arithmetic operations in one calculation problem.

Using the PMDAS acronym, there are no parentheses, but there is multiplication, therefore, you will multiply 6 x 5 first to get 30.

Then, again, using the PMDAS acronym, you would then add because there is no division in this equation so the division step can be skipped.

Using the PMDAS acronym, there are no parentheses, there is no multiplication, and there is no division, therefore, you will initially perform the addition.

Next, you would perform the calculation by subtracting 8 from 28.

Using the PMDAS acronym, there are no parentheses, there is no multiplication, but there is division, therefore, you will initially perform the division and then, in the correct sequence and order according to the PMDAS, calculate any addition and then, finally, any subtraction which is not present in this calculation.

Using the PMDAS acronym, there are parentheses and multiplication in this equation. You would, therefore, adhere to the correct sequential steps of PMDAS which are:

1. Parentheses
2. Multiplication
3. Division
5. Subtraction

You will begin by calculating the calculation in the parentheses which is 16 – 12.

You then perform the multiplication calculation as the final step in solving this equation.

Using the PMDAS acronym, there are parentheses, multiplication and addition in this equation. You would, therefore, adhere to the sequential steps of PMDAS and begin with the calculation within the parentheses as below.

Next, you have to calculate the multiplication as shown below.

Lastly, the addition is performed and calculated.

The first step is to perform the calculation within the parenthesis, as below.

The next step is to perform the multiplication, as below.

The next step, according to the PMDAS acronym is division, as shown below.

## 5.4: Four Operations with Rational Numbers - Mathematics

Rating: #### Common Core Standards

7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.1a - Describe situations in which opposite quantities combine to make 0.

7.NS.1b - Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.1c - Understand subtraction of rational numbers as adding the additive inverse,p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7.NS.1d - Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2 - Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.2a - Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.2b - Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2c -Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.2d - Convert a rational number to a decimal using long division know that the decimal form of a rational number terminates in Os or eventually repeats.

7.NS.3 - Solve real-world and mathematical problems involving the four operations with rational numbers.

Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Model with mathematics.

#### Description of Unit

The unit “Operations with Rational Numbers” from Georgia DOE focuses on understanding of operations of rational numbers. Students extend previous understanding of operating with fractions to adding, subtracting, multiplying, and dividing rational numbers. The unit is paced to 20-25 days and consists of 8 performance tasks. Each task is presented in a real-world context and allows students to develop their own strategies. Students model the operations of rational numbers in multiple ways and look for patterns in order to generate algorithms.

#### Cautions

Connecticut teachers should be aware that performance tasks do not identify which standards (content or practice) are being addressed. The unit does not include the following components:

• structures for implementing and completing performance tasks. There are no instructional notes (answer keys, rubrics, student work samples).
• differentiation or supports for students working above/below grade level, English language learners, or students with disabilities.
• a summative performance task or other type of summative assessment.
• There is only limited use of technology.

#### Rationale for Selection

• Unit materials can be embedded into existing units focused on operations using rational numbers.
• The exploratory nature of the lessons highlights the development of conceptual understandings
• The rigorous tasks are rooted in real-world contexts and situations
• There is evidence of rigor and coherence within the domain in the tasks.
• United States FULL
• Connecticut FULL

In Unit 4, sixth-grade students extend their understanding of numbers to include rational numbers. Prior to this unit, students have worked only with positive values, and their concepts of number lines and coordinate planes have been limited by these positive values. Students explore real-world situations that naturally connect to negative values, such as temperature, money, and elevation. The number line is a valuable tool that is referred to and used throughout the unit. Students use the number line to develop understanding of negatives, opposites, absolute value, and comparisons and inequalities (MP.5). They also discover the four-quadrant coordinate plane by intersecting two number lines at a 90-degree angle and representing locations using ordered pairs.

In elementary grades, students build and develop their sense of number with positive values. They use the number line as a tool to better understand whole numbers, fractions, and decimals. In fifth grade, students look at the first quadrant of the coordinate plane and represent locations using ordered pairs of positive numbers. In sixth grade, students build on and extend these concepts to include negative values.

In seventh grade, students will discover how to compute with rational numbers and what happens when the properties of operations are applied to negative values. The work they do in this sixth-grade unit is foundational of these seventh-grade concepts.

Pacing: 16 instructional days (13 lessons, 2 flex days, 1 assessment day)

For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 6th Grade Scope and Sequence Recommended Adjustments.

## Rational Number Word Problems

Videos, solutions, and lessons to help Grade 7 students learn how to solve real-world and mathematical problems involving the four operations with rational numbers.

### Suggested Learning Targets

• I can solve mathematical and real-world problems involving four operations with rational numbers. (Tom had pieces of rope. Rope 1 was 5 ½ feet long. Rope 2 was 74 inches long. Rope 3 was 1 ½ yards long. What is the total length of rope?)
• I can justify the steps taken to solve multi-step mathematical and real-world problems involving rational numbers.

Example 1: A recipe for trail mix calls for 3/4 cup dried fruits, 1/2 cup mixed nuts, and 1/3 cup granola. How many cups of trail mix does this recipe make?

Example 2: Anastasia was 19 1/4 inches at birth. At her 3 month checkup, she measures 23 1/2 inches. How much has she grown?

Example 3: The Darwin D. Martin house, built by Frank Lloyd Wright, has a rectangular stained glass window with a length of 41 1/2 feet and a width of 26 1/4 feet. What is the area of the window?

Example 4: You are an editor for your school yearbook. Each row of photos is 8 5/8 inches wide, including the margin. Each photo is 1 1/4 inches wide, the space between each photo is 1/8 inch, and each margin is 1/4 inch. How many photos can fit in one row?

2. A baker needs to make 8 batches of cookies for a party. If each batch requires 2 3/4 cups of flour, how many cups will he need?

3. Mike is putting up a fence in the back yard. The fence comes in sections that are 4 2/3 feet long. If the yard is 34 feet long, how many sections will he need to buy?

4. Bella volunteers to make cookies for her math class. Each batch of cookies requires 1 2/3 cups of flour. If she has 12 cups of flour, how many batches of cookies can she make? Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 