Question

1. without computing, decide whether the value of each expression is much smaller than 1, close to 1, or much greater than 1.

a. 100÷1/1000
b. 50 1/3÷50 1/4
c. 4.7÷5.2
d. 2÷7335
e. 2,000,001÷9
f. 0.002÷2,000

1. a rocking horse has a weight limit of 60 pounds.

a. what percentage of the weight limit is 33 pounds?
b. what percentage of the weight limit is 114 pounds?
c. what weight is 95% of the limit?

1. compare using >, =, or <.

a. 0.7_____0.70
b. 0.03 + 6/10_____0.30 + 6/100
c. 0.9_____0.12

Explanation:

3a. Analyze the division

Dividing by a fraction is multiplying by its reciprocal. $100\div\frac{1}{1000}=100\times1000 = 100000$, so it is much greater than 1.

3b. Use exponent - division rule

For $a^m\div a^n=a^{m - n}$, $50^{\frac{1}{3}}\div50^{\frac{1}{4}}=50^{\frac{1}{3}-\frac{1}{4}}=50^{\frac{4 - 3}{12}}=50^{\frac{1}{12}}$. Since $50>1$ and the exponent is positive, it is much greater than 1.

3c. Compare numerator and denominator

$4.7\div5.2=\frac{4.7}{5.2}$, and $4.7<5.2$, so it is much smaller than 1.

3d. Compare numerator and denominator

$2\div7335=\frac{2}{7335}$, and $2<7335$, so it is much smaller than 1.

3e. Compare numerator and denominator

$2000001\div9=\frac{2000001}{9}$, and $2000001>9$, so it is much greater than 1.

3f. Compare numerator and denominator

$0.002\div2000=\frac{0.002}{2000}$, and $0.002<2000$, so it is much smaller than 1.

4a. Use percentage formula

The percentage formula is $\text{Percentage}=\frac{\text{Part}}{\text{Whole}}\times100\%$. Here, the part is 33 pounds and the whole is 60 pounds. So $\text{Percentage}=\frac{33}{60}\times100\% = 55\%$.

4b. Use percentage formula

The part is 114 pounds and the whole is 60 pounds. $\text{Percentage}=\frac{114}{60}\times100\%=190\%$.

4c. Use percentage - of - a - number formula

To find 95% of 60 pounds, we use the formula $x = p\times w$, where $p = 0.95$ and $w = 60$. So $x=0.95\times60 = 57$ pounds.

5a. Compare decimal values

$0.7$ and $0.70$ are equal because $0.7=\frac{7}{10}$ and $0.70=\frac{70}{100}=\frac{7}{10}$. So $0.7 = 0.70$.

5b. Simplify and compare

$0.03+\frac{6}{10}=0.03 + 0.6=0.63$ and $0.30+\frac{6}{100}=0.30+0.06 = 0.36$. So $0.03+\frac{6}{10}>0.30+\frac{6}{100}$.

5c. Compare decimal values

$0.9=\frac{9}{10}$ and $0.12=\frac{12}{100}=\frac{3}{25}$. Since $\frac{9}{10}=0.9$ and $\frac{3}{25}=0.12$, $0.9>0.12$.

Answer:

3a. Much greater than 1
3b. Much greater than 1
3c. Much smaller than 1
3d. Much smaller than 1
3e. Much greater than 1
3f. Much smaller than 1
4a. 55%
4b. 190%
4c. 57 pounds
5a. =
5b. >
5c. >