Becky won silver on the uneven bars behind Belgium's Nina Derwael, while Ellie took bronze in the vault.
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Biles' vault gold was her 23rd world championships medal equalling Vitaly Scherbo's tally, but could only finish fifth in the uneven bars.
The American will look to become the outright most decorated gymnast when she takes place in the balanced beam and floor exercise on the final day of the championships on Sunday.
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