Indices Mixed Demonstration This resource provides animated demonstrations
- Slides: 45
Indices – Mixed – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.
Index (Indices) Power Base “ 2 to the power of 4” “ 2 to the 4” How do we describe this? What is it shorthand for? Exponent
When an index is applied to a fraction, we can apply the index to both the numerator & the denominator.
What is this calculation? Can we solve it with factorisation? 105 ÷ 15
Solving with factorisation
What pattern can you see? How can we complete the table? ÷ 2 ÷ 2 ÷ 2
What pattern can you see? How can we complete the table? ÷ 3 ÷ 3 ÷ 3
A negative indices means that instead of multiplying by the number many times, we divide by the number many times. A negative power is the reciprocal of the positive power.
A negative indices means that instead of multiplying by the number many times, we divide by the number many times.
How can we write this as a calculation? A negative indices will create the reciprocal , so a fraction will be ‘flipped’.
How can we write this as a calculation? A negative indices will create the reciprocal, so a fraction will be ‘flipped’.
How can we write this as a calculation? A negative indices will create the reciprocal, so a fraction will be ‘flipped’.
Square root According to the rules for multiplying indices, what is the result of this calculation? What does this tell us about the meaning of fractional indices? Square root Square number (invisible 2)
Cube root According to the rules for multiplying indices, what is the result of this calculation? What does this tell us about fractional indices? Cube root Cube number
How can we expand this fractional indices and write it as two calculations?
How can we expand this fractional indices and write it as two calculations?
Describe these in the form and as an integer.
Therefore, Do you agree?
Therefore, Do you agree?
When an index is applied to a fraction, we can apply the index to both the numerator & the denominator.
To manipulate surds we can split them into factors and take the square root of each. If we have the square root of a fraction, we can apply the square root to the denominator & numerator.
How can we split this index into two operations? Negative: reciprocal Take the reciprocal Fraction: root
How can we split this index into two operations? Negative: reciprocal Take the reciprocal Fraction: cube root
How can we split this index into three operations? Fraction: cube root Negative: reciprocal Integer: square Take the reciprocal
How can we split this index into two operations? Negative: reciprocal Take the reciprocal Fraction: root
How can we split this index into two operations? Negative: reciprocal Take the reciprocal Fraction: cube root
How can we split this index into three operations? Negative: reciprocal Fraction: cube root Integer: square Take the reciprocal
How can we split this index into three operations? Negative: reciprocal Fraction: square root Integer: cube Take the reciprocal
Calculating with Terms with Indices Multiplying Fractional (Unit) Fractional (Non-Unit) Division Brackets Negative Fractional Negative
Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk