Instruction 3-6

Round off Decimals | Compare and Order Positive and Negative Fractions, Decimals, Mixed Numbers  | Interpret and Use Ratios | Use Proportions to Solve Problems | Using LCM to Solve Fraction Problems | Calculate Percentages and Solve Problems

CALCULATE PERCENTAGES AND SOLVE PROBLEMS
CA GR6 NS 1.4 CA GR7 NS 1.6

What is a percentage?

A percentage of anything tells us how many parts in each hundred there are of the item we are referring to.

You can convert a percentage to a decimal by dividing the percentage by 100. So, 80% is equal to 0.80.

You can convert a decimal to a percentage by doing the opposite of converting a percentage into a decimal. So, to convert a decimal to a percentage, you multiply by 100 instead of dividing by 100.

To change a percentage to a fraction by placing the percentage over 100:

Don’t forget to reduce!

To change a decimal to a fraction, read the decimal in words and substitute numerals for words.

0.98 reads ninety eight hundredths = .

This can be reduced:

0.365 reads three hundred sixty five thousands =

This can be reduced:

Digits to the left of the decimal remain as whole numbers. For example:
To convert fractions to decimals, you divide the numerator by the denominator.

Since means 3 ÷ 15, you can carry out the division process and the result is a decimal:

Worksheet 1 Write the Percent.

Worksheet 2 Write the Percent.

Worksheet 3 Write the Percent.  

Worksheet 4 Write the Percent.  

Worksheet 5 Write the Percent.

Links for Students, Parents and Teachers

Now let's do Practice Exercise 3-6 (top)

Summary

Rounding Decimals

Remember rounding off decimals is exactly like rounding off whole numbers. To round to the nearest tenth, you do the same thing as when you round to the nearest whole number, except you work with a different place value.

To round to the nearest number use place-value. Look at the digit in the place to the right of where you want to round. Determine whether the digit is greater than 5 or less than 5. Round appropriately.

Comparing and Ordering Positive and Negative Numbers

Use place value to compare the numbers.
43.23; 43.32; 43.33

Compare the tens place. Then the ones place. When you compare the tenths place, you see that 43.23 is less than 43.32 and 43.33. Finally compare the hundredths place. 43.32 is less than 43.33. Therefore, the ordering of these numbers from least to greatest is 42.23, 43.32, 43.33.

To compare and order fractions and mixed numbers, you must first find the least common denominator of the fractions or mixed numbers that you are comparing. In order to find the lowest common denominator, you must find the least common multiple first.

The least common multiple of two or more whole number, the lowest whole number greater than 0 that is a multiple of each of the numbers.

The lowest common denominator is the least common multiple of the denominators of two or more fractions.

Interpreting Ratios

A ratio is a comparison of two quantities.

There are three types of ratios part to part, part to total, and total to part.

Part to part compares the red circles to the yellow circles. Part to part ratio is 2:5.
Part to total compares the red circles to the total amount of circles, 2:7 or you can compare the yellow circles to the total amount of circles, 5:7.
Finally, total to part compares the total amount of circles to the red circles, 7:2, or the total amount of circles to the yellow circles, 7:5.

Proportions

A proportion is an equation stating that two ratios are equivalent.
A cross product of two fractions is a product of the numerator of one fraction and the denominator of the other fraction.

If two ratios form a proportion, the cross products are equal.
For example, if  , then 4 x 15 = d x 5.

Also, if their cross products are equal, the two ratios form a proportion.
For example, if is a proportion, since 1 x 21 = 3 x 7; both are equal to 21.

To find out if the proportions are equal you need to find the cross product.

Calculating Percentages

Remember to convert a percentage to a decimal you divide the percent by 100. For example,
0.43 = 43%.

To change a percentage into a fraction, you place the percentage over 100. Don’t forget to reduce your fraction.

To change a decimal to a fraction, read the decimal in words and substitute numerals for words. The decimal 0.78 reads seventy-eight hundred. Therefore, 78 will be your numerator and 100 would be your denominator. Don’t forget to reduce your fraction.

Remember, digits to the left of the decimal remain as whole numbers:

To convert fractions to decimals, you divide the numerator by the denominator.

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