Properties of Operations with Rational Numbers
What property of operations is used when you multiply a number by its reciprocal to get 1?
The Inverse Property of Multiplication Property
If a recipe calls for 34\frac{3}{4}43 cup of sugar and you need to double the recipe, how much sugar do you need?
2 * 3/4 = 6/4 = 1.5 c
Simplify
4 + (3/5 - 1)
4+(-2/5 )=4− 2/5 =3.6
Convert 2.75 to a fraction.
2.75 =
11/4
If a shirt costs $30 and is on sale for 25% off, how much will it cost after the discount?
30 x 0.25 = $7.50 off.
New Price: 30 - 7.50 = $22.50
What is the result of dividing a negative number by a positive number?
The answer will be negative.
Sarah bought 3 shirts for $12.50 each. How much did she spend in total?
3 × 12.50= $37.50
Solve. -3 + 5 x 2
-3 + 10 = 7
Convert 7/8 to a decimal (no calculator)
0.875
If the ratio of boys to girls in a class is 3:4, how many girls are there if there are 12 boys?
Set up the proportion:
3/4 = 12/x
x:x = 16 girls
Apply the distributive property: What is 3 (4 + 1/2)?
3(4) + 3(1/2) = 12 + 3/2 = 13.5
A student earned $50 for babysitting. If they spend 2/5 of it on groceries, how much money did they spend on groceries?
2/5 * 50 = $20
A student runds 2 miles every day. How many miles will the student run in 3.5 weeks?
2 * 3.5 * 7 = 49 mi
If the estimated cost of a new phone is $350, and the actual cost is $360, is the estimation reasonable?
Yes, the estimation of $350 is very close to the actual cost of $360
If you buy 4 pencils for $1.20, what is the cost of 10 pencils?
1.20/4 = 0.30 per pencil
For 10 pencils: 0.30 x 10 = $3
What property of operations is demonstrated when you rearrange the terms in 5+(−2)=(−2)+5?
The Commutative Property of Addition
A car traveled 120 miles in 3 hours. What was its average speed?
120/3 = 40 mph
Solve:
1/4 + 3 * (2 + 1/2)
1/4 + 3 * 2.5 = 1/4 + 7.5 = 7.75
Convert 5.6 to a fraction.
5.6 = 28/5
A car can travel 120 miles on 8 gallons of gas. How far can it travel on 5 gallons of gas?
Set up the proportion:
120/8 = x/5
x:x = 75 miles
Which property is applied in (-7) x 1 = -7
The Identity Property of Multiplication.
ohn wants to buy 4.5 pounds of apples. If the apples cost $1.60 per pound, how much will he pay?
4.5 x 1.60 = $7.20
5/6 * (12 - 7/3)
5/6 * (12 - 2.33) = 5/6 x 9.67 = 8.06
Estimate the sum of 3.7 and 2.8
3 + 3 = 6
A recipe calls for 3/4 cup sugar for 8 servings. How much sugar would be needed for 12 servings?
Set up the proportion:
3/4/8 = x/12
x:x = 1.125 cups or 9/8 cups