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Fluently Add, Subtract, Multiply, and Divide Multi-Digit Decimals

Show your work for all problems. Include an estimation check where indicated.

Grade 6·22 problems·~40 min·Common Core Math - Grade 6·standard·6-ns-b-3
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which sum is correct for 35 + 214?

2.

What is 23 × 14?

3.

Estimate 4.8 + 3.2 by rounding each number to the nearest whole number. What is your estimate?

B

Fluency Practice

1.

Compute: 12.4+3.6712.4 + 3.67

2.

Compute: 8.05−3.78.05 - 3.7

3.

Compute: 2.3×1.42.3 \times 1.4

4.

Compute: 0.06×0.40.06 \times 0.4

5.

Compute: 1.32÷0.41.32 \div 0.4

C

Varied Practice

1.

Which correctly adds 3.5+2.143.5 + 2.14?

Vertical subtraction setup showing 10.00 minus 4.37 with decimal points aligned
2.

To subtract 10−4.3710 - 4.37, first rewrite the whole number as a decimal: 10=‾10 = \underline{\hspace{5em}}. Then subtract to get   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

10 as a decimal:
difference:
3.

What is 0.03×0.50.03 \times 0.5?

4.

Estimate 3.14×2.73.14 \times 2.7 by rounding each to the nearest whole number: estimate is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Now compute exactly:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

estimate:
exact product:
5.

To compute 5.76÷0.085.76 \div 0.08, a student multiplies the divisor by 100 to get 8. What must the student also do to the dividend?

D

Word Problems

1.

A grocery store sells apples for $0.89 each, oranges for $1.15 each, and bananas for $0.35 each. Priya buys 2 apples, 1 orange, and 3 bananas.

1.

What is the total cost of Priya's fruit? Show your addition.

2.

Estimate the total cost by rounding each item price to the nearest dollar. What is your estimate?

2.

A roll of ribbon is 9.45 meters long. It is cut into 3 equal pieces.

How long is each piece?

3.

A car travels 13.72 kilometers on 4 liters of fuel.

How many kilometers does the car travel per liter of fuel?

4.

A box of cereal weighs 0.42 kg. A store has 15 such boxes.

What is the total weight of all 15 boxes?
Estimate:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   kg
Exact total:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   kg

estimate:
exact total:
E

Error Analysis

1.

Lena added 4.3+1.254.3 + 1.25 by right-aligning the digits instead of the decimal points. She wrote:

  1. Aligned rightmost digits: the 3 in 4.3 under the 5 in 1.25
  2. Added: 43+125=16843 + 125 = 168
  3. Placed a decimal point one place from the right: 16.816.8

Lena's answer: 16.816.8

What error did Lena make?

2.

Amara multiplied 2.3×1.42.3 \times 1.4 and correctly computed 23×14=32223 \times 14 = 322. Then she counted the decimal places in the product: "322 has 3 digits, so I need 3 decimal places." She wrote 0.3220.322.

What error did Amara make?

F

Challenge / Extension

1.

Compute 0.008×0.050.008 \times 0.05 exactly and write the equivalent fraction.
Decimal:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
Fraction:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

decimal product:
fraction form:
2.

Explain why dividing 5.76÷0.085.76 \div 0.08 gives the same result as 576÷8576 \div 8. Use the idea of equivalent fractions in your explanation.

0 of 22 answered