Place Value & Powers of 10
What is the value of the digit 7 in 472,615?
70,000 — seventy thousand
Calculate 324 × 6.
1,944
Complete the equation: 2/3 = ?/12.
8/12
Evaluate: 18 + 6 × 4.
42. Multiply first: 6 × 4 = 24; then 18 + 24 = 42.
How many grams are in 3 kilograms?
3,000 grams. Each kilogram equals 1,000 grams.
Write 10 × 10 × 10 × 10 using an exponent.
10⁴
Calculate 247 × 32.
7,904.
Calculate 3/4 + 2/3
9/12 + 8/12 = 17/12 = 1 5/12.
Evaluate: (45 − 21) ÷ 6 + 7.
11. First 45 − 21 = 24; then 24 ÷ 6 = 4; finally 4 + 7 = 11.
A rope is 8 meters long. How many centimeters long is the rope?
800 centimeters. 8 × 100 = 800.
Calculate 6,240 × 100.
624,000
Calculate 5,616 ÷ 24.
234.
Calculate 5 1/6 − 2 3/4.
31/6 − 11/4 = 62/12 − 33/12 = 29/12 = 2 5/12.
Insert parentheses to make this equation true: 8 + 4 × 3 = 36.
(8 + 4) × 3 = 36.
A class collects 245 cans on Monday and 378 cans on Tuesday. They pack all the cans equally into 7 boxes. How many cans go in each box?
245 + 378 = 623; 623 ÷ 7 = 89 cans per box.
Calculate 830,000 ÷ 1,000.
830
Calculate 3,847 ÷ 26. Give the quotient and remainder.
Quotient = 147; remainder = 25
A ribbon is 6 1/2 feet long. A student cuts off 2 3/4 feet. How much ribbon remains?
6 1/2 − 2 3/4 = 6 2/4 − 2 3/4 = 3 3/4 feet.
Compare using >, <, or =:
50 − (12 + 8) ___ 50 − 12 + 8.
<. The left side is 30; the right side is 46
A recipe uses 2 1/4 cups of flour for one batch of muffins. How many cups of flour are needed for 3 batches?
2 1/4 × 3 = 6 3/4 cups.
A student says 450 × 10³ = 4,500. Explain the mistake and give the correct product.
The student did not multiply by 1,000. Since 10³ = 1,000, the correct product is 450,000.
A school orders 28 boxes of pencils. Each box contains 144 pencils. The pencils are shared equally among 32 classrooms. How many pencils does each classroom receive?
28 × 144 = 4,032 pencils. Then 4,032 ÷ 32 = 126 pencils per classroom
Four students share 3 pizzas equally. What fraction of a pizza does each student receive? Explain how you know.
3 ÷ 4 = 3/4 of a pizza per student. Divide each pizza into 4 equal pieces; each student gets 3 pieces of size 1/4.
A student evaluates 6 × (20 + 5) − 10 as 6 × 20 + 5 − 10 = 115. Explain the mistake and find the correct answer.
The student did not multiply both terms inside the parentheses by 6. The correct calculation is 6 × 25 − 10 = 150 − 10 = 140.
A school buys 8 bags of rice weighing 425 grams each and 6 bags of beans weighing 350 grams each. Students use 1,500 grams of food. How many grams remain?
Rice: 8 × 425 = 3,400 g. Beans: 6 × 350 = 2,100 g. Total: 5,500 g. Remaining: 5,500 − 1,500 = 4,000 grams.