Math Lesson 60 Equations With Fractions

Solve x - 1/3 = 5/6 1. Add 1/3 to each side 2. Find the LCD 3. Add and simplify

1. Add 1/3 to each side 2. Find the LCD 3. Add and simplify

mix number

A number made up of a whole number that is not zero and a fraction.

fraction

A number that expresses part of a set or whole.

whole number

Doesn't contain a fraction. A whole number is an integer which has 1 or more units and can be positive or negative.

Solve j + 1/4 = 2 7/16 a. 1/4 b. 2 11/16 c. 2 3/16 d. 2 2/7

c. 2 3/16

Solve using mental math. 8 5/9 = n + 5 2/9 a. 8 5/9 b. 5 5/9 c. 3 1/3 d. 13 7/9

c. 3 1/3

solve using mental math x - 1/7 = 3 4/7 a. 2 5/7 b. 3 3/7 c. 3 5/7 d. 3 4/7

c. 3 5/7

mental math

Thinking through and solving math problems without using a paper and pencil or a calculator.

Using Mental Math to Solve Equations

You can sometimes use mental math to solve equations that involve fractions or mixed numbers.

Name the two ways to solve equations with a variable and two fractions. How would you decide which way was best or easiest to find the missing variable?

You can use mental math or inverse operations to solve the equation. The way I would solve it is by using mental math because it is easier for me.

Solve j + 3/5 = 2 8/15 a. 1 14/15 b. 1 7/8 c. 3 2/15 d. 1/3

a. 1 14/15

Irene's gas tank was 9/10 full when she left her house, and it was 7/15 full when she arrived for her vacation. What fraction of a tank of gas did she use driving there? a. 13/30 of a tank b. 1/2 of a tank c. 2/3 of a tank d. 2/5 of a tank

a. 13/30 of a tank

Solve x - 1/4 = 4/8 a. 3/4 b. 1/2 c. 1 1/3 d. 1 1/2

a. 3/4

Solve each equation using mental math. a. 5 5/6 - x = 2 1/6 b. 14 1/4 + x = 25 1/2

a. 5 5/6 - x = 2 1/6 x = 3 4/6 = 3 2/3 b. 14 1/4 + x = 25 1/2 14 1/4 + x = 25 2/4 x = 11 1/4

Complete 9 = 8 ?/6 a. 6 b. 8 c. 4 d. 12

a. 6

solve j + 1/2 = 4 9/14 a. 5 1/7 b. 4 1/7 c. 1/7 d. 1 5/9

b. 4 1/7

A roll of wrapping paper is 84 inches long. You cut lengths of 23 1/2 inches and 15 1/4 inches to wrap two gifts. How much paper is left? a. 38 3/4 inches b. 45 1/4 inches c. 46 1/4 inches d. 75 3/4 inches

c. 45 1/4 inches

Find the sum. 2 1/10 + 4 3/5 a. 10/67 b. 1 2/3 c. 6 7/10 d. 13 2/5

c. 6 7/10

x - 1/3 = 5/6 a. 2 1/3 b. 6/7 c. 5/6 d. 1 1/6

d. 1 1/6

solve using mental math 6 8/9 = n + 5 4/9 a. 12 1/3 b. 5 8/9 c. 6 8/9 d. 1 4/9

d. 1 4/9

Solve using mental math. q - 4 5/7 = 5 4/7 a. 5 5/7 b. 1 3/4 c. 6/7 d. 10 2/7

d. 10 2/7

Identify the subtraction problem that does not need to be renamed before subtracting. a. 7 - 2 1/2 b. 9 1/3 - 4 2/3 c. 6 3/10 - 2 7/10 d. 3 5/8 - 2 3/8

d. 3 5/8 - 2 3/8

Write and solve. One and one-half years ago, Steven was 5 years old. How old is he now?

n - 1/2 = 5; 6 1/2 years old

Solve x + 3 1/8 = 15 7/8 using mental math.

x = 12 6/8 x + 12 3/4 1. find the missing whole number 2. find the missing fractions 3. simplify 12 6/8 + 3 1/8 = 15 7/8

For the equation x - 3/8 = 5/16, rewrite the equation using like denominators.

x- 3/8 = 5/16 x - 6/16 = 5/16 x = 11/16

Write and solve. If Jason spends 2 1/2 hours more at camp, he will complete 9 hours of camp counseling. How many hours has he worked as a counselor so far?

9 - 2 1/5; 9 - 2 = 7 He has worked 6 4/5, so if you were to round it, he would have worked about 7 hours.

Solving equations with fractions

You can also use inverse operations to get the variable alone on one side of the equation. Then write the answer in simplest form.

Solve using mental math. q - 5 5/7 = 6 6/7 a. 6 5/7 b. 12 4/7 c. 1 1/6 d. 1 1/7

b. 12 4/7

In the equation x - 1/3 = 2/9, what is the least common multiple of 3 and 9? a. 3 b. 9 c. 19 d. 27

b. 9