Question

1. 5 cm = ____ m
2. estimate: what percent of 51 is 32?

60%
keeping skills sharp

1. 261 - 194 =
2. 9.73 - 2.41 =
3. $\frac{5}{7} \times \frac{1}{4} =
4. 110% of 99 is what number?
5. what is the prime factorization of 39?
6. find the least common multiple of 28 and 70.
7. what is the perimeter of a regular hexagon whose sides are 52 cm?
8. simplify: 7 + 49 ÷ 7
9. round 0.619 to the nearest hundredth.
10. $4^2 + 9 \times 6 - 4 =$

Explanation:

Step1: Subtract the two integers

$261 - 194 = 67$

Step2: Subtract the decimals

$9.73 - 2.41 = 7.32$

Step3: Multiply the fractions

$\frac{5}{7} \times \frac{1}{4} = \frac{5 \times 1}{7 \times 4} = \frac{5}{28}$

Step4: Calculate percentage of number

First convert 110% to decimal: $110\% = 1.1$
Then calculate: $1.1 \times 99 = 108.9$

Step5: Find prime factors of 39

Divide 39 by smallest prime: $39 = 3 \times 13$ (both 3 and 13 are primes)

Step6: Find LCM of 28 and 70

Prime factorize:
$28 = 2^2 \times 7$
$70 = 2 \times 5 \times 7$
Take highest powers: $2^2 \times 5 \times 7 = 4 \times 5 \times 7 = 140$

Step7: Calculate hexagon perimeter

Regular hexagon has 6 equal sides: $6 \times 52 = 312$ cm

Step8: Simplify using order of operations

First divide: $49 \div 7 = 7$, then add: $7 + 7 = 14$

Step9: Round to nearest hundredth

Look at thousandths place (9 ≥5), so round up hundredths place: $0.62$

Step10: Simplify using order of operations

First exponent: $4^2 = 16$
Then multiply: $9 \times 6 = 54$
Now compute: $16 + 54 - 4 = 66$

Answer:

1. $67$
2. $7.32$
3. $\frac{5}{28}$
4. $108.9$
5. $3 \times 13$
6. $140$
7. $312$ cm
8. $14$
9. $0.62$
10. $66$