Grade 3

• 1. Make both denominators the same by multiplying both denominators by each other, 2. Then multiply the numerator by whatever you multiplied the denominator by, 3. Add or subtract the numerators across ( leave the denominator the same. 4. Finally, if the number is a improper fraction or can be simplified, simplify it
• when multiplying mixed numbers, you first need to convert the mixed number into an improper fraction. Then you need to multiply the numerator and denominator.
• When dividing fractions first make sure that there are no mixed numbers and make sure that that both fractions are either proper or improper. then use KCF which means you keep the first fraction the same, change to divide sign to a multiply and finally flip the final fraction. then multiply across.
• what does KCF mean

  Keep, Change, Flip
• If you want to decrease a number by a percentage : for example 10 decreased by 20% you need to do 100 x 0.80 = 80
• If you want to increase a number by a percentage : for example 100 increased by 20% you need to do 100 x 1.20 = 120
• if you want to share an amount into a ratio ( for example: 9:2 = 11) you then need to add up all the parts and divide by the total amount. Finally multiply the number you got by the amount of parts ( 9 x *) (2 x *)
• To convert a fraction to a decimal you just divide the numerator by the denominator.
• to convert a fraction to a percentage you just divide the numerator by the denominator and multiply by 100
• to convert a decimal to a percentage you just multiply by 100
• To convert a percentage to a decimal divide the percentage by 100
• to find a percentage of a number you must divide the Percentage by the total value and then multiplying the result by 100. 
• To multiply decimals, we multiply them just like whole numbers. We count the number of digits behind the decimal in both numbers we're multiplying, and make sure our answer has the same number of digits after the decimal
• How to find a fraction of an amount:

  1. Divide the amount by the denominator.
  2. Multiply the answer by the numerator.
• The reciprocal of a number is 1 divided by the number. It can also be found by raising the number to the power of −1. The reciprocal, also called the multiplicative inverse, is found by writing the original number as a fraction and “flipping” it.
• To expand a bracket means to multiply each term in the bracket by the expression outside the bracket
• In order to factorise an algebraic expression into a single bracket:

  1. Find the highest common factor of each of the terms in the expression.
  2. Write the highest common factor (HCF) at the front of a single bracket.
  3. Fill in each term in the bracket by multiplying out.
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• find the HCF for each expression, write the HCF outside the brackets, and then simplify the expression

  
• Rules for angles in parallel lines include1234:

  • Corresponding angles are equal.
  • Alternate angles are equal.
  • Allied angles add up to 180°.
  • Angles adjacent to each other on a straight line add up to 180º.
  • Vertical angles/ Vertically opposite angles are equal.
  • Pair of interior angles on the same side of the transversal are supplementary.
  • When two lines intersect, their opposite angles are equal.
• The sum of the interior angles of any polygon can be found using the formula: sum of interior angles = (number of sides – 2) × 180°
• 1. Locate the point you are measuring the bearing from and draw a north line if there is not already one given.
  2. Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.
  3. Draw a line from the start point in the direction of the bearing.
  4. Always measure bearings from the North line.
  5. Always express your answers as three-figure bearings (so 60degree would be 060degree).
  6. Always draw and measure bearings clockwise.
• • Define the line of reflection (a mirror line) that the shape is reflected over.
  • Describe how the shape is flipped over the mirror line to create a mirror image.
  • Explain that each new point is the same distance from the mirror line as the original point.
  • Provide an example of a shape reflected over a mirror line.
• • Divide the shape into simpler shapes, such as rectangles, triangles, or squares.
  • Find the area of each simpler shape, using the formula for that shape. For example, the area of a rectangle is base × height.
  • Add the areas of the simpler shapes together to get the total area of the compound shape.
  • If the compound shape has any parts that are removed, subtract the area of those parts from the total area.
• In order to calculate the perimeter of compound shape: Work out any missing lengths. Add all the side lengths. Write the final answer with the correct units.
• Formulas prism n number of edges volume V = A b ⋅ h surface area A = 2 ⋅ A b + A l

  
• The formula for the volume of a prism is obtained by taking the product of the base area and height of the prism. The volume of a prism is given as V = B × H where, "V" is the volume of the prism, "B" is the base area of the prism, and "H" is the height of the prism.
• To calculate the area of a triangle, you can use different methods depending on the information you have:

  • If you know the base and the height of the triangle, you can multiply them and divide by 2.
  • If you know the lengths of all three sides of the triangle, you can use Heron's formula, which involves calculating half of the perimeter and then taking the square root of a product.
  • If you know the lengths of two sides and the angle between them, you can multiply the sides and the sine of the angle and divide by 2
• To calculate the perimeter of a triangle you need to add the lengths of the sides. The formula for the perimeter is P= a+b+c where p is the perimeter and a,b,c are the sides
• 1. Find the radius of the circle, which is half the diameter.
  2. Use the formula Area of a circle = πr2, where π is about 3.14159 and r is the radius.
  3. Multiply π by the square of the radius.
  4. Give your answer with the correct units, such as square meters or square centimeters.
• The diameter is the length of the circle
• The circumference is the perimeter of a circle.
• • Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.
  • Multiply the diameter of the circle with π (pi).
  • Multiply 2×radius with pi (π=3.14).
  • Use the formula C = πd, where "C" represents the circumference of the circle, and "d" represents its diameter
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