# 5.9: Division of Fractions - Mathematics

5.9: Division of Fractions - Mathematics

## What is 5/9 divided by 2? - Fractions Division getcalc.com's fractions division calculator is an online basic math function tool to find what's the equivalent fraction for dividing 5/9 by a whole number 2. In mathematics, every integer is a rational number, hence a whole number 2 can be written as 2/1.
5/9 ÷ 2 = 5/18 in fraction form.

5/9 ÷ 2 = 0.2778 in decimal form.
This calculator, formula, step by step calculation and associated information for fraction 5/9 divided by 2 may help students, teachers, parents or professionals to learn, teach, practice or verify such division between two fractions calculations efficiently.

## Dividing Fractions Worksheets

Thorough and structured, our printable worksheets on dividing fractions help children stop foraging for resources to practice and learn how to divide fractions. Access our pdf practice resources to give the learners in grade 5, grade 6, and grade 7 a newfound drive to divide fractions with other fractions, whole numbers, and mixed numbers. Remind them to use the answer key to double-check the solutions. Get the would-be mathematicians ready to roll with our free dividing fractions worksheets! Drive home the fact that the simple rule of dividing by fractions is to flip and multiply. Encourage children to practice consistently so the task of dividing fractions and whole numbers is not a puzzler anymore! Enable kids to say goodbye to any confusion that arises while dividing two fractions! Let them invert the second fraction and multiply it with the first. Simplify the fractions whenever required. Children in 5th grade and 6th grade are expected to find the missing numerator or denominator by isolating the incomplete fraction on one side and multiplying the fractions on the other. These pdf worksheets on dividing fractions impel students to divide mixed numbers. Convert the mixed numbers into fractions and proceed to multiply the dividend with the reciprocal of the divisor. Continue to intrigue and inspire the aspiring math wizards with heaps of exercises on dividing mixed numbers by fractions. Ensure that they flip only the 'divisor' fraction and perform multiplication. Have the zesty learners mastered the skill of dividing fractions by mixed numbers? Find out by persuading grade 6 and grade 7 students to solve these printables featuring fractions and mixed numbers. Up for grabs is an exciting collection of word problems on fraction division! When children add copious practice to bountiful learning, not only do the fun scenarios feel relatable, they become easy to solve.

## Fractions in the real world

Fractions surround our everyday activities. Here are some examples of fractions in real life:

Eating at a restaurant: Think about a time you go to a restaurant with friends and the waitress brings a single bill. To divide the total amongst the friends, you use fractions.

Shopping: Think about the time you went shopping for a new school bag. There was half off on everything due to a sale, so you calculate the new price using fractions.

Following a recipe: Recipes sometimes suggest using (frac<1><2>) a teaspoon of sugar, (frac<3><4>) tablespoon of salt. Some recipes also have quantities to serve 2. If we are making the same dish to serve 3 people, fractions are used to adjust the ingredients accordingly.

Sports: Fractions are frequently used to analyze the performance of a particular player and team.

Fitness: We use fractions to understand our body mass index (BMI) to determine whether we are in a healthy range of body mass or not.

Drinks: To make drinks like mocktails, different fractions of liquids are mixed in the right amounts to get the best outcome.

Pizza: Dividing the pizza slices equally amongst everyone requires fractions.

Photography and videography: The shutter speed of a camera is calculated using fractions.

Tests and exams: Scores of tests and exams are generally expressed as fractions, like (frac<18><20>) .

Medical Prescriptions: When someone is sick, the doctor prescribes different dosages for people of various sizes. A full-grown adult may consume 500mg whereas a child may consume half of that.

Progress or decline: Progress or decline of any project can be measured. If the sales of a particular product are down by 25% or by (frac<1><4>) th.

Time: Half n hour is a common way of expressing 30 minutes. You can find some more of our blogs here:

## Solution

We show the long division process on the most difficult of these fractions, namely $frac<1><12>$: Notice that the remainder after subtracting $8 imes 12$ (hundredths) is the same as the remainder after subtracting $3 imes 12$ (thousandths), namely 4. This means that the 3 in the decimal repeats: we continue to take away 3 groups of 12 (in the ten thousandths place, hundred thousandths place, and so on) and the remainder is always 4. The decimal expansions of all of the fractions are listed below (those which repeat can be found in the same way as $frac<1><12>$ above and those which terminate are found when the long division process ends):

The fractions with terminating decimals on the list are: $frac<1><2>, frac<1><4>, frac<1><5>, frac<1><10>.$ The only prime factors of the denominators for each of these fractions are 2 and/or 5.

Taking $frac<1><4>$ as an example, we can see where the terminating decimal comes from by observing that $4$ is a factor of $100$: specifically we use the fact that $4 imes 25 = 100$.

The last equality comes from the fact that dividing by 100 moves the decimal two places to the left.

The fractions with repeating decimals on the list are: $frac<1><3>, frac<1><6>, frac<1><11>, frac<1><12>, frac<1><15>.$ Each of these fractions has a prime factor different from 2 or 5 in the denominator: 3, 6, 12, and 15 have a prime factor of 3 and 11 has a prime factor of 11. Unlike in the cases in part (b), multiplying by a power of 10 will never result in a whole number here because a factor of 3 or 11 will always remain in the denominator. This means that the decimals do not terminate.

## Simplifying fractions

Simplifying a fraction means to rewrite the fraction as an equivalent fraction, so that the numerator and denominator are as small as possible.

Like equivalent fractions, you can simplify a fraction if its numerator and the denominator have a common factor.

We can divide both numerator and denominator by this number to create a simplified fraction that is equivalent to the original fraction.

You keep simplifying a fraction until the numerator and denominator don’t have a common factor anymore – this is its simplest form.

1. Simplify ( frac<14> <22>)

Both (14) and (22) are divisible by (2) , so we can divide both top and bottom:

(7) and (11) don’t have any common factors. So, this is its simplest form.

1. Do both the numerator and denominator have a common factor?
1. Yes – Divide both numerator and denominator by this number
2. No – This is the fraction’s simplest form.

We usually look for the highest common factor when simplifying fractions. Don’t worry if you can’t identify it at first, you can always continue simplifying the fraction.

2. Simplify ( frac<56> <64>)

This looks like a hard fraction to simplify, but we can start off with an easy factor: (2).

Dividing both numerator and denominator by (2):

Now it’s a little easier to identify common factors.

(28) and (32) are both divisible by (4), so:

(7) and (8) don’t have a common factor.

So, this (frac<7><8>) is the simplest form!

## Using fractions to show ratios

You can use a fraction to show a ratio. In a ratio, the numerator shows the part of a group you are considering and the denominator show the rest of the group or the whole group.

Suppose a class has 6 boys and 10 girls. What is the ratio of boys to girls. In this example, the numerator is the number of boys and the denominator is the rest of the group or the number of girls.

What is the ratio of girls to the total number of students? In this case, the numerator is the number of girls and the denominator is the whole group or the total number of students

## What is an equivalent fraction? How to know if two fractions are equivalent?

Finding equivalent fractions can be ease if you use this rule:

Equivalent fractions definition: two fractions a b and c d are equivalent only if the product (multiplication) of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

In other words, if you cross-multiply ( a b and c d ) the equality will remain, i.e, a.d = b.c . So, here are some examples:

• 10 18 is equivalent to 5 9 because 10 x 9 = 18 x 5 = 90
• 15 27 is equivalent to 5 9 because 15 x 9 = 27 x 5 = 135
• 20 36 is equivalent to 5 9 because 20 x 9 = 36 x 5 = 180

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