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# How to subtract mixed fractions with whole numbers

## How to subtract mixed fractions with whole numbers

This article breaks down the concept, defines important terms, presents a clear, step-by-step subtraction method, and solidifies understanding through practical examples. Perfect for students seeking to master the intricacies of fraction arithmetic.

## Introduction to Whole Numbers

Whole numbers are the set of all non-negative integers. Starting from zero, they extend indefinitely towards positive infinity. The set of whole numbers is represented as ${0, 1, 2, 3, 4, 5, 6, …}$.

These numbers are used frequently in everyday computations such as counting items, performing arithmetic operations, and setting order. Whole numbers do not have any fractional or decimal parts.

## Definition of Mixed Fractions

A mixed fraction is a whole number and a proper fraction combined. It is called ‘mixed’ because we are mixing whole numbers and fractions. For example, in $2\frac{1}{3}$, $2$ is the whole number, and $\frac{1}{3}$ is the fractional part.

Mixed fractions are commonly used in daily life. For instance, when measuring quantities that are not whole, like $1\frac{1}{2}$ kilograms of sugar or $3\frac{3}{4}$ meters of cloth.

## Steps to Subtract Mixed Fractions from Whole Numbers

Subtracting mixed fractions from whole numbers can seem a bit daunting at first, but once the steps are understood, it’s straightforward. The process involves three main steps:

### Step 1: Convert the Whole Number to an Equivalent Fraction

Whole numbers can be converted into fractions by using 1 as the denominator. For example, the whole number $4$ can be written as a fraction $\frac{4}{1}$.

### Step 2: Convert the Mixed Fraction to an Improper Fraction

An improper fraction is a fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number).

A mixed fraction can be converted to an improper fraction by:

1. Multiplying the whole number by the denominator of the fractional part.
2. Adding the numerator of the fractional part to the product obtained in step 1.
3. Keeping the denominator as is.

### Step 3: Perform the Subtraction

With the whole number and the mixed fraction now both represented as fractions, it’s possible to subtract one from the other. If the denominators of the fractions are not the same, find a common denominator by multiplying the two denominators. Subtract the numerators of the two fractions. Simplify the resulting fraction, if possible, by converting it back into a mixed number.

## Sample Questions on how to subtract mixed fractions with whole numbers

Let’s put these steps into practice:

Problem 1: Subtract $2\frac{1}{3}$ from $4$

1. Convert the whole number to a fraction: $4 = \frac{4}{1}$
2. Convert the mixed fraction to an improper fraction: $2\frac{1}{3} = \frac{7}{3}$
3. Make denominators same: $\frac{4}{1} = \frac{12}{3}$
4. Perform the subtraction: $\frac{12}{3} – \frac{7}{3} = \frac{5}{3}$
5. Convert back to a mixed number: $\frac{5}{3} = 1\frac{2}{3}$

So, $4 – 2\frac{1}{3} = 1\frac{2}{3}$.

Problem 2: Subtract $3\frac{1}{2}$ from $6$

1. Convert the whole number to a fraction: $6 = \frac{6}{1}$
2. Convert the mixed fraction to an improper fraction: $3\frac{1}{2} = \frac{7}{2}$
3. Make denominators same: $\frac{6}{1} = \frac{12}{2}$
4. Perform the subtraction: $\frac{12}{2} – \frac{7}{2} = \frac{5}{2}$
5. Convert back to a mixed number: $\frac{5}{2} = 2\frac{1}{2}$

So, $6 – 3\frac{1}{2} = 2\frac{1}{2}$.

## Subtracting mixed fractions with whole numbers practice problems

Problem 1:

Subtract $2\frac{1}{2}$ from $5$.

Convert the whole number to a fraction: $5 = \frac{5}{1}$
Convert the mixed fraction to an improper fraction: $2\frac{1}{2} = \frac{5}{2}$
Make denominators same: $\frac{5}{1} = \frac{10}{2}$
Perform the subtraction: $\frac{10}{2} – \frac{5}{2} = \frac{5}{2}$
Convert back to a mixed number: $\frac{5}{2} = 2\frac{1}{2}$
So, $5 – 2\frac{1}{2} = 2\frac{1}{2}$.

Problem 2:

Subtract $4\frac{2}{3}$ from $10$.

Convert the whole number to a fraction: $10 = \frac{10}{1}$
Convert the mixed fraction to an improper fraction: $4\frac{2}{3} = \frac{14}{3}$
Make denominators same: $\frac{10}{1} = \frac{30}{3}$
Perform the subtraction: $\frac{30}{3} – \frac{14}{3} = \frac{16}{3}$
Convert back to a mixed number: $\frac{16}{3} = 5\frac{1}{3}$
So, $10 – 4\frac{2}{3} = 5\frac{1}{3}$.

Problem 3:

Riya had $7$ apples. She ate $2\frac{1}{2}$ apples in the morning. How many apples does she have left?

Riya had $7$ apples. She ate $2\frac{1}{2}$ apples in the morning. How many apples does she have left?

Using the same method as Problem 1, you find that Riya has $7 – 2\frac{1}{2} = 4\frac{1}{2}$ apples left.

Problem 4:

A piece of ribbon is $9$ meters long. $4\frac{3}{4}$ meters of ribbon is used to make a bow. How many meters of ribbon are left?

A piece of ribbon is $9$ meters long. $4\frac{3}{4}$ meters of ribbon is used to make a bow. How many meters of ribbon is left?

Following the same steps, the length of the ribbon left is $9 – 4\frac{3}{4} = 4\frac{1}{4}$ meters.

Problem 5:

A marathon is $26\frac{1}{5}$ miles long. After running $16$ miles, how many more miles does a runner need to complete to finish the marathon?

A marathon is $26\frac{1}{5}$ miles long. After running $16$ miles, how many more miles does a runner need to complete to finish the marathon?
Using the same method, the runner still needs to run $26\frac{1}{5} – 16 = 10\frac{1}{5}$ more miles to finish the marathon.