body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

Cumulative Practice

Exercise 13 Page 233

Call the number x and write an equation that represents the situation from the exercise using x.

G

We know that the sum of one-third of a number and 10 is equal to 13 and we want to find the number. Let's call the number x. One third of the number x can be expressed as 13 times x. 1/3 xThe sum of one third of x and 10 is equal to 13. This means that 13x plus 10 equals 13. 1/3x + 10 = 13 We want to find the number x. Let's use inverse operations to solve the above equation.

1/3x + 10 = 13

LHS-10=RHS-10

1/3x+10-10=13-10

Subtract terms

1/3x = 3

LHS * 3=RHS* 3

3*1/3x=3*3

DenomMultFracToNumber

3 * a/3= a

x=3*3

Multiply

x=9

We found that x=9. This means that the number we are looking for is 9. This corresponds to option G.

Extra

Inverse Operations

Inverse operations are two operations that, all else being equal, undo one another. For instance, adding 6 and subtracting 6 are inverse operations because they cancel each other out. &x + 6 - 6 &x + 6 - 6 &x When using inverse operations and the Properties of Equality, any operation performed on one side of the equation must also be performed on the other side of the equation to maintain equality. x÷2 &=1 x÷2 * 2&=1 * 2 x&=2 In this case, the division by 2 on one side of the equation can only be eliminated by multiplying 2 on both sides of the equation. The result of applying the Properties of Equality on an equation is an equivalent equation.

Subchapter links

Exercises