Fractions <-> Decimals
Convert to a decimal:
14\frac{13}{25}
14\frac{13}{25}=14\frac{52}{100}=14.52
Write in standard form:
1.21\times 10^5
121,000
Last night, I had dinner with three of my friends. Our total bill was $45.64. If we split the bill evenly, how much did we each contribute?
45.64 \div 4 = $11.41
3\frac{2}{3}\div 6\frac{7}{8}
3\frac{2}{3}\div 6\frac{7}{8} = \frac{11}{3}\div\frac{55}{8}= \frac{11}{3}\times \frac{8}{55}=\frac{8}{15}
Ms. Miller's class has a 4:3 ratio of girls to boys. If there are 35 students in the class, then how many of them are girls?
Ratio of girls to all students is 4:7 = 20:35, so there are 20 girls in the class.
Convert to a mixed number in simple form.
99.0088
=99\frac{88}{10000}
= 99\frac{11}{1250}
Write in scientific notation:
1000.24
1.00024\times 10^3
John spent \frac{2}{5} of his paycheck on a video game, and \frac{1}{3} of the remaining money on snacks. If he had $35 left, how much did he have to begin with?
Bar model -> $87.50 to start with
0.11^3
0.001331
Three children shared a box of chocolates in the ratio 7:8:11. If the largest share was 66 chocolates, how many chocolates were in the smallest share?
Equivalent ratio 42:48:66 -> smallest share is 42 candies.
Convert to a decimal:
\frac{999}{1125}
\frac{999}{1125} = \frac{111}{125} = \frac{888}{1000}=0.888
Write in scientific notation:
0.00329\times \frac{1}{10^9}
0.00329\times \frac{1}{10^9} = 3.29\times \frac{1}{10^3}\times\frac{1}{10^9} = 3.29\times \frac{1}{10^12}
Tom multiplied a number by 2\frac{1}{2} correctly, and got 50 as an answer. However, he was actually supposed to divide the number by 2\frac{1}{2} . What answer should he have gotten?
If the original number was x, the correct answer was x\div2\frac{1}{2}=50\div2\frac{1}{2}\div2\frac{1}{2} = 8
Evaluate:
3.2-3.2\div (0.4\div0.008)
3.2-3.2\div (0.4\div0.008)
= 3.2-3.2\div50
=3.2-0.064
=3.136
An 8-inch long sandwich is cut into two pieces whose lengths are in the ratio 7:5. How long is the shorter piece?
The shorter piece should be
\frac{5}{12}
of the whole sandwich.
\frac{5}{12}\times 8 = \frac{10}{3}=3\frac{1}{3}
True or False? If true, explain. If false, provide a counterexample.
If a fraction's denominator is 222, it has a repeating decimal representation.
False! e.g. 111/222 = 1/2 = 0.5
222/222 = 1
Write in scientific notation:
(3*10^6)\div (5*\frac {1}{10^9})
(3*10^6)\div (5*\frac {1}{10^9})= \frac{3*10^6}{5*\frac{1}{10^9}}
\frac{3}{5}\times\frac{10^9}{\frac{1}{10^9}}
=0.6\times(10^6*10^9)
= 0.6\times10^{15}
=6\times10^{14}
Jules used a calculator to divide x by y, and found a quotient of 1.0625. Both x and y were whole numbers less than 50, but he can't remember what the were. Find all possible values of x and y.
\frac{x}{y}
must be equivalent to
\frac{17}{16}
. Only choices where both numbers are whole numbers less than 50 is x = 17, y = 16 or x = 34, y = 32
Evaluate:
19.87^2-19.87\times 9.88+0.1987
= (19.87)(19.87)-(19.87)(9.88)+(19.77)(0.01)
= 19.87(19.87-9.88+0.01)
= 19.87(10)
= 198.7
Reduce to lowest terms:
66^3:88^3
66^3:88^3 = \frac{(2*3*11)^3}{(2^3*11)^3} = \frac{2^3*3^3*11^3}{2^9*11^3} = \frac{3^3}{2^6} = \frac{27}{64}
Use >,<,= to compare:
\frac{25}{26} and 0.\overline{962}
\frac{25}{26} <0.\overline{962}
\frac{25}{26}=0.961... or 0.\overline{962}=\frac{26}{27}
One inch is approximately 1.578\times \frac{1}{10^5} miles. One centimeter is about 6.214\times\frac{1}{10^6} miles. How many miles bigger is one inch than one centimeter? Give your answer in scientific notation!
1.578\times\frac{1}{10^5}-6.214\times\frac{1}{10^5}
= 15.78\times\frac{1}{10^6}-6.214\times\frac{1}{10^6}
=(15.78-6.214)\times\frac{1}{10^6}
9.566\times\frac{1}{10^6}
miles
10 jugs of water can fill \frac{5}{8} of a bucket. An additional 4 jugs and 5 cups of water are needed to fill the remaining part of the bucket. How many cups of water can the bucket hold?
Bar model -> 40 cups
0.\overline{80}\div 0.\overline{72}
0.\overline{80}\div 0.\overline{72} = \frac {80}{99} \div \frac{8}{11} = \frac {80}{99}*\frac{11}{8}=1\frac{1}{9}
45 rocks are divided into three piles in the ratio \frac {1]{6}:\frac{1}{3}:\frac{1}{4}
How many rocks are in the smallest pile?
10 rocks
\frac {1]{6}:\frac{1}{3}:\frac{1}{4} = 2:4:3
\frac{2}{9} = \frac {10}{45}