Fraction of a Number and Mixed Numbers Worksheets

Fractions of a number, such as 3/4 of 12, and mixed numbers, such as 1 3/4, are the last steps of grade 4 fractions. The four PDFs on this page have pictures of equal groups, fractions of a number, improper fractions to mixed numbers, and both directions, with answer keys. They follow standards 4.NF.B.3 and 4.NF.B.4 of the Common Core standards for grade 4 fractions.

Quick answer: To find a fraction of a number, divide the number by the bottom of the fraction, then multiply by the top: 3/4 of 12 is 12 ÷ 4 = 3, then 3 × 3 = 9. A mixed number, such as 2 1/3, is a whole number and a fraction. This page has 4 free printable worksheets with answer keys for grades 4 and 5. Updated October 2026.

Finding a fraction of a number

To find 3/4 of 12, share 12 into 4 equal groups (3 in each), then take 3 of the groups: 9. In short: divide by the denominator, multiply by the numerator. The picture worksheets let children circle the groups before they learn the shortcut.

Mixed numbers and improper fractions

An improper fraction has a numerator bigger than its denominator, like 7/4. It is more than one whole: 4/4 makes 1 whole, with 3/4 left over, so 7/4 = 1 3/4. To go back, multiply the whole number by the denominator and add the numerator: 1 × 4 + 3 = 7, so 1 3/4 = 7/4.

Fractions of a number worksheets: what is in the set

There are 4 fractions of a number worksheets on this page, and every one has an answer key except for any cut-out games. The first two sets are about fractions of a number, and the last two sets change between improper fractions and mixed numbers.

Fraction of a number worksheets: share, then multiply

The fraction of a number worksheets teach one rule: divide the number by the denominator, then multiply by the numerator. To find 3/4 of 12, share 12 into 4 equal groups, which gives 3 in each, and then take 3 groups, which is 9. The fraction is an instruction: the denominator says how many equal groups, and the numerator says how many groups to take. This is also how the standard 4.NF.B.4 describes a fraction of a quantity, as a multiple of a unit fraction. This table shows eight examples:

The order does not matter for the answer, since 3 × 12 ÷ 4 is also 9, but dividing first keeps the numbers small. Wikipedia’s article on fractions explains why multiplying by a fraction and finding a fraction of a number are the same thing.

Fractions of a number: which numbers work?

Fractions of a number come out as whole numbers only when the number is a multiple of the denominator. This is the reason why the worksheets use 12, 18, 24, 36 and 40, and not 13 or 25. The table shows how many numbers from 1 to 100 work for each denominator from 2 to 10:

A denominator of 2 works for half of the numbers and a denominator of 4 for a quarter of them. A denominator of 7 works for only 14 of the numbers, so the worksheets leave it for later. The times tables worksheets page is the best help, because the multiples of the denominator are the numbers that work.

The number 24 works for the denominators 2, 3, 4, 6, 8 and 12, which makes it a favorite for fractions of a number. This table shows eleven fractions of 24:

Fraction of a set worksheets: pictures first

The fraction of a set worksheets have pictures of counters or objects, and children circle equal groups to find the fraction of the number. For 12 counters and the fraction 3/4, they circle 4 equal groups of 3, then color 3 of the groups, and count 9 colored counters. This table shows six pictures, with the groups and the counters in each:

The picture is a bridge between the first page in the series, the identifying fractions page, where children name the fraction of a set, and the number sentence. After a few weeks children can answer without drawing, since the division and the multiplication are the same steps as the groups.

Fractions of amounts in real life

Fractions of amounts are used for money, time, weight and length, and it is helpful for children to see these in context. A discount of 1/4 off $20, 3/4 of an hour, and 2/3 of a recipe all use the same two steps. This table shows eight everyday examples:

These are also good examples for the money worksheets and telling time worksheets pages, where fractions of a dollar and fractions of an hour are used with coins and clocks.

Mixed numbers worksheets: a whole number and a fraction

The mixed numbers worksheets use numbers such as 1 3/4, which are a whole number and a fraction written together. Every mixed number can also be written as an improper fraction, with the numerator greater than the denominator. To change a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The denominator stays the same. This table shows six examples:

The check is to turn the improper fraction back: 7/4 is 4/4 and 3/4, which is 1 3/4. The picture of a bar for each whole and a part-bar for the fraction makes the idea clear, and the same picture is on the number line, where a mixed number is a point between two whole numbers.

Improper fractions to mixed numbers: divide and find the remainder

To change improper fractions to mixed numbers, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator over the same denominator. For 17/5, 17 ÷ 5 = 3 R2, so the mixed number is 3 2/5. The division worksheets page has the division facts, and the remainder idea is the same as in division with remainders. This table shows eight examples:

If the remainder is zero, the answer is a whole number: 12/4 = 3. A fraction with a numerator that is a multiple of the denominator is a whole number in disguise, and the fractions on a number line page shows these as points on the number line.

Multiplying a whole number by a fraction

Standard 4.NF.B.4 also asks for a whole number times a fraction, such as 3 × 2/5. This is repeated addition: 2/5 + 2/5 + 2/5 = 6/5, which is 1 1/5. This table shows six examples:

Finding a fraction of a number, such as 2/5 of 15, is the same as multiplying: 2/5 × 15 = 6. Grade 5 extends this to a fraction times a fraction, as described in the Common Core standards for grade 5 fractions.

Common mistakes with fractions of a number and mixed numbers

Most mistakes come from mixing up the two steps, or from forgetting what the remainder means. Here are five mistakes, with what went wrong and the fix:

Fractions of a number word problems

Fractions of a number are used for sharing and for amounts of money. Ask children to find the unit fraction first, and to write the working in two steps:

Games and activities for fractions of a number

Children learn fractions of a number best when they play with it. These games use things that are found at home or in a classroom:

• Group and circle: put 12 counters on the table, and ask the child to find 1/3, 2/3 and 3/4 of them
• Fraction shops: a sale of 1/4 off or 1/2 off, with price tags in dollars
• Mixed number race: turn cards to make an improper fraction, and the first to write it as a mixed number wins
• Dozen fractions: use an egg carton of 12 to find fractions of 12
• Measuring cups: fill a 1/3 cup five times, and write the amount as an improper fraction and as a mixed number
• Fraction bingo: a bingo card with whole-number answers, and calling cards with fractions of a number

Extra support and extra challenge with fractions of a number

For children who need more support: use counters and a picture of equal groups for every problem. Start with 1/2 and 1/4 of small numbers, and then move to thirds. Ask “how many equal groups?” before the child divides. For mixed numbers, use bars: one whole bar for each whole number, and part of a bar for the fraction.

For children who need more challenge: ask for the number that has 3/5 equal to 18, for a mixed number between 4 and 5 with a denominator of 8, and for 5/6 of 7 1/2. The worksheet that changes between the two forms is a good challenge, and so is the question “is 3/4 of a number always smaller than the number?”.

How to tell that a child is ready to move on from fractions of a number

1. The child divides by the denominator and multiplies by the numerator.
2. The child changes an improper fraction to a mixed number.
3. The child changes a mixed number to an improper fraction.
4. The child solves a story problem with a fraction of an amount.

When all four are true, move on to grade 5 fractions: unlike denominators, and the Common Core standards for grade 5 fractions that describe multiplying fractions.

A 20-minute lesson on fractions of a number

A short lesson is the best way to introduce fractions of a number. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where fractions of a number fits across the grades

No skill stands alone. This table shows what children learn before and after fractions of a number, with the standard that goes with each step:

Fractions of a number are a bridge to multiplication of fractions. The whole sequence is on the fractions worksheets page.

Helping at home with fractions of a number

Parents do not need to be experts to help with fractions of a number. These suggestions work well, and each takes only a few minutes:

• Ask “what is 1/4 of 20 dollars?” when shopping.
• Use 12 eggs or 24 crayons to find 1/3, 1/4 and 1/2.
• Look at a recipe: a half batch uses half of each amount.
• Turn improper fractions into mixed numbers while measuring in cups.
• Ask the child to explain the two steps in their own words.

How to check progress in fractions of a number

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for fractions of a number

Most children need about a week of short sessions for fractions of a number. This plan follows the order of the worksheets on this page:

When the plan is complete, the child is ready for grade 5 fractions. The whole sequence is on the fractions worksheets page.

Multiplying fractions by whole numbers worksheet

Finding a fraction of a number is the same as multiplying a fraction by a whole number: 3/4 of 12 means 3/4 × 12. A multiplying fractions by whole numbers worksheet asks children to multiply the numerator by the whole number and then divide by the denominator. When the answer is not a whole number, write it as a mixed number. Six examples:

Fraction times whole number worksheet and fraction and whole number multiplication

This page is also searched as a fraction times whole number worksheet, fraction times a whole number worksheet, fraction and whole number multiplication worksheet, multiplying fractions times whole numbers worksheets, multiplying fractions and whole numbers worksheet, multiply whole numbers and fractions worksheet and multiplying whole numbers and fractions worksheets. The fraction of a number pages above cover the whole number result, and the mixed numbers pages cover answers such as 2 2/3. Use each worksheet with the answer key, and check by drawing the fraction of a set.