16 pointsNot answered
Calculate: 2.89 × 6.37 + 3.63 × 2.89.
Grade 5 Enrichment · Assessment
Lesson 1.5 — Chapter 1 Exercise
Clever Decimal Calculations: practice with worked explanations.
Exercise directions
- Try the questions. Enter your answers and show your working where requested.
- Submit your attempt. Choose Submit exercise & open review when you are ready.
- Review and improve. Use the help available for this submission. Edit the original answer fields, then submit again.
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Two extra challenge skills
Questions 13 and 15 extend the chapter with systematic counting and rounding. Try these optional warm-ups before starting if either skill is new.
Prepare for Question 13: list possibilities without missing any
Use 1, 2, and 3 once each to form three-digit whole numbers. Start with the hundreds digit, then list the remaining digits in order.
Starting with 1: 123, 132. Starting with 2: 213, 231. Starting with 3: 312, 321.
There are 3 choices, then 2, then 1: 3 × 2 × 1 = 6. A list organized by the first digit helps you avoid duplicates. In Question 13, also check the last-digit rule.
Prepare for Question 15: compare a number with its rounded value
12.4 rounds to 12, so the original is 0.4 greater than the rounded value. 11.5 also rounds to 12, so that original is 0.5 less.
Draw a number line from 11.5 to 12.4 in steps of 0.1. Every point rounds to 12. Which endpoint gives the largest original number? Which gives the smallest?
For several numbers, add their individual differences from the rounded values. You do not have to guess the numbers one by one.
Short-answer questions
Questions 1–10 · 6 points each · 60 points total
26 pointsNot answered
Calculate:
2015 × (2.3 × 47 + 2.4) ÷ (2.4 × 47 − 2.3)
36 pointsNot answered
Calculate: 15.48 × 35 − 154.8 × 1.9 + 15.48 × 84.
46 pointsNot answered
Calculate:
(8.4 × 2.5 + 9.7) ÷ (1.05 ÷ 1.5 + 8.4 ÷ 0.28)
56 pointsNot answered
Calculate: 8 × (3.1 − 2.85) × 12.5 × (1.62 + 2.38).
66 pointsNot answered
Calculate:
0.9 + 9.9 + 99.9 + 999.9 + 9999.9 + 99999.9 + 999999.9
76 pointsNot answered
Calculate:
(4.8 × 7.5 × 8.1) ÷ (2.4 × 2.5 × 2.7)
86 pointsNot answered
Split the original decimal number into its whole-number part and its fractional part (a value from 0 up to, but not including, 1). Adding the original whole-number part to 4 times the fractional part gives 5.4. Adding that same whole-number part to 9 times the fractional part gives 8.4. What is the original decimal number?
What this operation means: for 2.7, the parts are 2 and 0.7. Adding 2 to four copies of 0.7 gives 4.8. The multiplied fractional part may exceed 1; you still add the original whole-number part, 2.
96 pointsNot answered
Xiaoming was supposed to divide a number by 3.75, but he read the division sign as a multiplication sign and obtained 225. What is the quotient he should have obtained by dividing the original number by 3.75?
106 pointsNot answered
The sum of numbers A and B is 303.49. Moving the decimal point in B one place to the left gives A. Find both numbers.
Extended-response questions
Questions 11–15 · 12 points each · 60 points total · Show your reasoning
1112 pointsNot answered
Calculate: 12.5 ÷ 3.6 − 7 ÷ 9 + 8.3 ÷ 3.6.
1212 pointsNot answered
Fill the box with a suitable number so that the equation is true:
[25 + 54.9 ÷ (□ − 2.37)] × 2.1 = 115.5
1312 pointsNot answered
Using the digits 1, 0, 7, 9 once each, together with a decimal point, how many numbers less than 10 can be formed that have exactly three decimal places and do not end in 0? Numbers below 1 are allowed: you may use 0 as the digit before the decimal point. Write all the numbers in increasing order.
1412 pointsNot answered
Find the value of:
(2 + 3.15 + 5.87) × (3.15 + 5.87 + 7.32)− (2 + 3.15 + 5.87 + 7.32) × (3.15 + 5.87)
1512 pointsNot answered
Five numbers each have exactly one decimal place, and none has 0 in the tenths place. Round each number to the nearest whole number: tenths 0–4 round down, and tenths 5–9 round up. The five rounded results have a sum of 98. The five original numbers do not have to be different. Round each number separately, not their sum. What is the greatest possible sum of the original five numbers? What is the least possible sum?
Finished your attempt?
Check your reasoning against the worked solutions. Your entered answers stay in place. Use the available review help to improve your method as well as your final answer.
Test view: worked solutions are hidden.
The section structure, numbering, values, expressions, and point allocations are preserved.
Lesson 1.5 — Chapter 1 Exercise: Answer Sheet
This printed sheet records your responses. Review the reasoning as well as the final answers.
Section A · Questions 1–10
| Question | Entered answer |
|---|