Ratios/ Proportions
A comparison of two quantities by division
What is a ratio?
Define Equivalent Expressions
Expressions that have the same value for all values of the variables.
What did the triangle say to the circle?
"You're pointless!"
An equation that states that two ratios are equivalent.
Proportion
Define an equation.
A mathematical sentence that shows two expressions are equivalent.
You are given 3 positive numbers. You can add these numbers and multiply them together. The result you get will be the same. Which are the numbers?
1,2 and 3.
1+2+3 = 6
1x2x3=6
A relationship between two quantities in which the ratio of one quantity to the other quantity is constant.
What is a proportional relationship.
Define Expression.
A mathematical phrase that contains operations, numbers, and/or variables.
Can you prove that seven is half of 12?
7+7=12
The Roman numeral for 7 is VII can be made by "cutting" the Roman numeral 12 (XII) in half. horizontally.
Define Percent
A Ratio comparing a number to 100.
A multi-digit number is expressed in this form when it is written as a sum off single-digit multiples of powers of ten.
What is Expanded Form.
Five different whole numbers add up to 15. Multiply those same five numbers together, and the result is 120.
Can you determine what those 5 numbers are?
1,2,3,4,5
1+2+3+4+5 =15
1x2x3x4x5=120
Define Unit Rate
A rate in which the second quantity in the comparison is one unit.
A mathematical sentence that shows the relationship between quantities that are not equivalent.
Inequality.
Seven houses each have seven cats. Each cat kills seven mice. Each of the mice, if alive, would have eaten seven ears of wheat. Each ear of wheat produces seven measures of flour.
How many measures of flour were saved by the cats?
16,807 measures of flower.
That's 7x7x7x7x7 or 7^5.
This puzzle comes from the ancient Egyptian "Rhind Papyrus" was written by the scribe Ahmes in 1850 B.C. Perhaps the world's oldest puzzle, it has inspired a great many variations over the thousands of years since its creation.