Unit 5, Lesson 4
Adding and Subtracting Decimals with Many Non-Zero Digits
Grade 6
4.1
Warm-up
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Clare bought a photo for 17 cents and paid with a $5 bill. Which of these three ways of writing the numbers could Clare use to find the change she should receive? Be prepared to explain your reasoning.
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Find the amount of change that Clare should receive. Explain or show your reasoning.
4.3
Activity
Write the missing digits in each calculation so that the value of each sum or difference is correct. Be prepared to explain your reasoning.
Third calculation. 0 point 7 minus an unknown quantity with four digits is equal to 0 point 0 1 2.
Fourth calculation, 7 minus an unknown quantity with five digits is equal to 3 point 4 5 6 7.
Fifth calculation, 70 minus an unknown quantity with six digits is equal to 0 point 0 0 8 9.
Student Lesson Summary
Base-ten diagrams work best for representing subtraction of numbers with few non-zero digits, such as . For numbers with many non-zero digits, such as , it would take a long time to draw the base-ten diagram. With vertical calculations, we can find this difference efficiently.
Thinking about base-ten diagrams can help us make sense of this calculation.
A setup for the subtraction calculation 0 point 2 5 1 0 3 subtract 0 point 0 4 6 7 1 results in 0 point 1 0 4 3 2. The number 0 point 2 5 1 0 3 is on top with the subtract 0 point 0 4 6 7 1 beneath, and the 0 from the first number lines up vertically with the 0 from the second number, the 2 from the first number lines up vertically with the 0 from the second, the 5 from the first number lines up vertically with the 4 from the second, and so on. The 1 in the thousandths place of the first number is unbundled to make ten groups of ten thousandths. The five in the hundredths place has 1 unbundled to make 4 hundredths and 10 thousandths.
The thousandth in 0.25103 is decomposed to make 10 ten-thousandths so that we can subtract 7 ten-thousandths. Similarly, one of the hundredths in 0.25103 is decomposed to make 10 thousandths.
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