Grade6 Numsense
1. **State the problem:** Understand place values and write the value of underlined digits.
2. **Step a:** 4 in 4,582,307 is in the millions place, so the place value is million.
3. **Step b:** 4 in 7,345 is in the tens place, so the place value is tens.
4. **Step c:** 2 in 98,025 is in the tens place, so the place value is tens.
5. **Write numbers in words:**
- a) 345,678 can be read as "three hundred forty-five thousand six hundred seventy-eight." The parts 3 hundreds, 4 tens, 5 ones relate to digits in the thousands section.
6. **Express number in standard form:** "Three million, twenty-five thousand, nine." is written as $3,025,009$.
7. **Comparisons:**
- a) $563,201 > 562,901$ because $563,201 - 562,901 = 300 > 0$.
- b) $45.70 = 45.70$, they are equal.
8. **Order numbers:** Arrange $453,999$, $458,732$, $482,307$ from least to greatest:
$$453,999 < 458,732 < 482,307$$
9. **Decimal values of underlined digits:**
- a) In $3.7\underline{1}5$, digit 1 is in the hundredths place so value is $0.01$
- b) In $0.4\underline{2}9$, digit 2 is in the hundredths place so value is $0.02$
10. **Order decimals ascending:** $0.5 < 0.503 < 0.53$
11. **Write 0.6 in words:** "six tenths"
12. **Convert fractions to decimals:**
- a) $\frac{1}{2} = 0.5$
- b) $\frac{3}{4} = 0.75$
13. **Convert decimals to fractions:**
- a) $0.25 = \frac{1}{4}$
- b) $0.6 = \frac{3}{5}$
14. **Convert fraction to decimal percentage:** $\frac{1}{2} = 50\%$
15. **Operations with whole numbers:**
- a) $345 + 256 = 601$
- b) $720 - 458 = 262$
16. **Multiply:** $234 \times 5 = 1170$
17. **Divide:** $482 \div 7 = 68 \text{ remainder } 6$ which equals $68 \frac{6}{7}$
18. **Operations with decimals:**
- Add: $2.5 + 3.45 = 5.95$
- Subtract: $6.3 - 2.8 = 3.5$
- Multiply: $2.4 \times 0.6 = 1.44$
- Divide: $4.8 \div 0.12 = 40$
19. **Convert to percentages:**
- a) $0.25 = 25\%$
- b) $\frac{3}{4} = 75\%$
20. **Convert percentages to decimals:**
- a) $50\% = 0.50$
- b) $25\% = 0.25$
21. **Calculate sale price:** 25% off $40 = 40 \times 0.25 = 10$ discount, so pay $40 - 10 = 30$
22. **Percent of 25 out of 100:** $\frac{25}{100} \times 100 = 25\%$