# Fraction of a number

### Fraction of a number

#### Lessons

In this lesson, we will learn:

• How to understand fraction of a number using: models with shapes, models with fraction blocks, and fraction number lines
• The steps for multiplying a fraction with a whole number

Notes:

• When we are looking for a fraction of a number, we are using multiplication
• The word “of” in math usually signifies multiplication

• We can use models with shapes to find the fraction of a number:
• Ex. What is $\frac{1}{5}$ of 15?
• Use 15 circles to represent the whole number; divide into 5 equal parts; answer how many circles are in 1 of those parts:

Therefore, $\frac{1}{5}$ x 15 = 3

• We can also use models with fraction blocks to find the fraction of a number:
• Ex. What is $\frac{2}{3}$ × 5?
• Create a fraction block with 2 of 3 equal parts shaded in. Repeat 5 times.

• There are 10 parts shaded in, each one is worth $\frac{1}{3}$ of a whole.
• Therefore, $\frac{2}{3}$ x 5 = $\frac{10}{3}$ or 3 $\frac{1}{3}$

• We can also use number lines to find the fraction of a number:
• Ex. What is 4 × $\frac{1}{5}$ ?
• Split a line (from 0 to 1) into 5 equal parts, create 4 jumps of 1 part each ($\frac{1}{5}$)

• Generally, the fastest way to find the fraction of a number will be to do fraction multiplication with a whole number using these steps:

• Step 1: Put the whole number as a fraction over 1
Step 2: Cross cancel the numbers if possible
Step 3: Multiply the top numbers and then separately multiply the bottom numbers
Step 4: Write your answer in lowest terms
• Ex. What is $\frac{6}{18}$ of 24?
• Introduction
Introduction to Fraction of a Number:
a)
Fraction of a number using shapes

b)
Fraction of a number using fraction blocks

c)
Fraction of a number using number lines

d)
The 4 steps for fraction multiplication with a whole number

• 1.
Number Lines and Fraction of a Number
Use the number line to complete the multiplication sentence (fill in and/or analyze):
a)
5 × $\frac{1}{8}$ = ___

b)
$\frac{2}{5}$ x 6 = ___

c)

d)

• 2.
Fraction Blocks and Fraction of a Number
Use fraction blocks to solve for the fraction of each number.
a)
4 × $\frac{1}{6}$ = ?

b)
$\frac{2}{3}$ × 6 = ?

c)
Which model shows the answer to $\frac{1}{9}$ × 5?

d)
Which model shows the answer to 3 x $\frac{3}{5}$ × 5?

• 3.
Fraction Multiplication for Fraction of a Number
Use the steps for fraction multiplication to solve.
• Hint: (1) put whole number over 1, (2) cross cancel, (3) multiply numerators; multiply denominators, (4) write in lowest terms
a)
14 × $\frac{1}{7}$ = ?

b)
$\frac{3}{11}$ × 11 = ?

c)
6 × $\frac{4}{5}$ = ?

d)
$\frac{2}{35}$ × 70 = ?

e)
48 × $\frac{9}{16}$ = ?

f)
Ben lives $\frac{53}{24}$ miles away from the mall. Trixie lives 6 times that distance from the mall. How many miles away from the mall does Trixie live?

• 4.
Figuring out Fraction Multiplication Backwards
Fill in the blanks by working backwards.
a)
? × $\frac{1}{8}$ = 6

b)
$\frac{5}{26}$ × ? = $\frac{5}{26}$

c)
? × $\frac{1}{9}$ = 0

d)
? × $\frac{3}{4}$ = 6

e)
$\frac{6}{20}$ × ? = 7$\frac{1}{2}$

• 5.
Fraction of a Number Picture Problems
Use the picture. Write the multiplication equation with a fraction and a whole number. Then, solve for the fraction of a number.
a)

b)

c)

• 6.
Fraction of a Number: Word Problem
Jerry Jepson Elementary School has a population of 380 students. Mrs. Kim's class has 14 girls and 10 boys.
a)
If $\frac{1}{6}$ of the class is vegetarian, how many students are vegetarian?

b)
If $\frac{3}{8}$ of the class has siblings, how many students have a brother or sister? How many students are only-children?

c)
If $\frac{7}{38}$ of the school's students have pets how many students have pets? Out of these pet owners, $\frac{4}{7}$ have dogs as pets; how many students have dogs?

d)
If $\frac{3}{5}$ of the school wears glasses and $\frac{1}{4}$ of Mrs. Kim's class wears glasses, what is the FRACTION of students wearing glasses in the class compared to the entire school?