Math Flashcards
What five steps would you use to solve the problem below:
In a classroom, the ratio of boys to girls is 4:3. If there are 28 boys, how many girls are there?
- Write as equation: 4:3 = 28:x
2: Write as fractions: 4/3 = 28/x
3: Cross multiply: 4x = 84
- Divide 4 on both sides to find x: x = 21
- Solution: 21 girls
What five steps would you use to solve the problem below:
The ratio of apples to oranges in a basket is 3:2. If there are 30 fruits in total, how many apples and how many oranges are there?
- Write as equation: 3x + 2x = 30
- Add x’s: 5x = 30
3: Divide 5 on both sides to find x: x = 6
- Multiply the value of x to the ratios: 3(6); 2(6)
- Solution: apples = 18; oranges = 12
What six steps would you use to solve the problem below:
The product of two whole numbers is 36, and their ratio is 1:4. What is the smaller number of the ratio?
- Write as equation: 1x * 4x = 36
- Multiply x’s: 4x^2 = 36
3: Find the square root: 2x = 6
- Divide 2 on both sides to find x: x = 3
- Multiply the value of x to the ratios: 1(3); 4(3)
- Solution: 3:12; smallest number is 3.
What two steps would you use to solve the problem below:
A meter was cut at the 35-cm mark. What is the ratio of the smaller piece to the larger piece?
- Find the length of the other half: If a meter is 100 cm, then 35:65
- Simplify the ratio by dividing by 5: Answer = 7:13
What five steps would you use to solve the problem below:
If ₽75.00 is shared among three children in the ratio of 3:7:15. The size of the smallest share is?
- Write equation: 3x + 7x + 15x = 75
- Add the x’s: 25x = 75
- Divide 25 on both sides to find x: x = 3
- Multiply the value of x to the ratios = 3(3):7(3):15(3)
- Solution: Smallest share is 9
How do you know if a number is divisible by 2?
If it ends in 0,2,4,6, or 8.
Even numbers are usually divisible by 2.
How do you know if a number is divisible by 3?
If the sum of all digits is divisible by 3.
How do you know if a number is divisible by 4?
If the last two digits are divisible by 4
How do you know if a number is divisible by 5?
If the number ends in 0 or 5
How do you know if a number is divisible by 6?
If it is divisible by 2 and 3
How do you know if a number is divisible by 7?
- You multiply the last digit of the number by 2.
Ex: 252 = 2*2 = 4
- You subtract the result to the remaining digits.
Ex: 25-4 = 21
- If the end result is divisible by 7, then it is divisible by 7.
Ex: 21/7 = 3
How do you know if a number is divisible by 8?
If the number formed by the last 3 digits is divisible by 8.
If a number ends in 000, is it divisible by 8?
Yes.
How do you know if a number is divisible by 9?
If the sum of all digits is divisible by 9.
How do you know if a number is divisible by 11?
Three steps:
- Add all the numbers in the odd places.
- Add all the numbers in the even places.
- Subtract the results from Steps 1 and 2.
If the difference is divisible by 11, then it is divisible by 11.
How do you know if a number is divisible by 12?
If the number is divisible by both 3 and 4.
How do you add two numbers with different signs?
You subtract their base values then adopt the sign of the bigger number.
-8 + (+4) = -4
Why does the result adopt a negative sign?
Because the bigger number (8) uses a negative sign.
8 + (-4) = 4
Why does the result adopt a positive sign?
Because the bigger number (8) uses a positive sign.
When we simplify equation from -12 - (-7), to -12 + 7
Why does 7 eventually turn into a positive sign?
Because negative signs beside each other cancel each other out and turn positive.
How do you find the area of a square?
side^2
How do you find the area of a rectangle?
length * width
How do you find the area of a right triangle?
ab/2
How do you find the hypotenuse of a right triangle?
c^2 = a^2 + b^2
