Embedded Files
Ratios
Simplifying Ratios
Ratios compare quantities. To simplify a ratio, divide all parts by their highest common factor (HCF) — just like simplifying a fraction.
Example: simplify 20: 30: 40. the HCF (highest common factor) is 10 so divide each number by 10 so it will be 2: 3: 4
Practice Problem:
Simplify the ratio 16:24:56
Answer: HCF is 8 so divide all by 8 = 2:4:7
Dividing a Quantity in a Given Ratio
To divide something like money or ingredients into a ratio, follow these steps:
Step-by-step to divide $120 in the ratio 1:3
Add the parts: 1+3=4
Divide 120 by 4 → each part is 30
Give 1 part to the first person = $30
Give 3 parts to the second = $90
Adapting Recipes Using Proportion:
Let's assume you want to bake cookies and the recipe says that it's made for 4 people. However, you want to bake cookies for 10 people. So, you want to adjust the given recipe to make it serve 10 people.
Multiply Every Ingredient by That Factor
Suppose the original recipe uses: 2 eggs, 100g sugar, 300 ml milk
Now multiply everything by 2.5 (your scaling factor):
Eggs → 2×2.5=5 eggs
Sugar → 100×2.5=250 g
Milk → 300×2.5=750 ml
Now the recipe feeds 10 instead of 4!
Using Map Scales
A scale of 1:50,000 means 1 cm on the map = 50,000 cm in real life
Example: a road is 3.2 cm on the map. What's the real length?
3.2×50,000=160,000 cm=1.6 km
Best Value
Find which product gives more for your money.
Example: Pack A: which is a better offer 500g for $4 or Pack B: 750g for $5.50?
Answer: find the price per gram. Pack A: 4/500 = 0.008 $/gram and Pack B: 5.50/750 = 0.0073 $/gram. So, Pack B has the better offer
Speed = Distance ÷ Time
Speed questions are the most common.
Example: a car travels 300 km in 5 hours
Speed= 300/5 = 60 km/h
Don’t forget: always convert minutes to hours if your speed is in km/h!
Practice Problem:
A cyclist travels 45 km in 3 hours 45 minutes.
Answer: convert time into hours:3 hours 45 min = 3.75 hours
Then: speed = 45/3.75 = 12 km/h
Exchange Rates
If 1 USD = 0.75 GBP, then to convert $80: 80×0.75=60 GBP
This is done through cross-multiplication (multiply the numerator of 1 fraction by the denominator of the 2nd fraction → num1 x den 2 = den 1 x num2):
Page updated
Google Sites
Report abuse